IUTđÇŢ˝ßĚpę ..
167:PRQlÚĚfłń
21/10/01 16:43:05.25 9nXmqzo6.net
>>166
ÂĂŤ
ľŠľAęĘŢĚ_Íą¤˘Á˝ŕĚĆÍŮČéTOđp˘AťĚ\Ź@ŞCÓĚĺćĚÉξĤÜ@\ˇéć¤ÉľČŻęÎČçȢB
qxgĚLźČâčŞXČéWĚhĆČÁÄAŘĺĄAtBbvEtgFO[AG~[EAeBAw[gEnbZŮŠ˝ÉćéíXĚÝĽŞąŠęéąĆĆČÁ˝BľdvČŘĚśÝčŞ1920NÉmçęASÄĚĺvČĘÍ1930N˛ëÜĹÉÍoťëÁĢ˝BŘžłęé׍ĂTIČ\zĚĹăĚęÂÍPťčipęĹjĹ Á˝BŢĚ_ĚĹĚŘžÉÍAćČđÍwIč@Şp˘çę˝B1930NăČ~ÍAłŔłgĺĆťĚKQÉÖˇéHtKNENĚ_ŞLřĹ éąĆŞćÉFßçęĢBąĚ_Í|g[MoÎŤĆŃ¢ÄASIČĘĹ éAeBĚÝĽĚćčŰIČčŽťŞŞŠčŐČÁ˝BdvČiKÍA1930NăÉN[hEV
@[ÉćÁÄCf[Şąüłę˝ąĆĹ éBCf[đCfAŢĚăíčÉp˘éąĆĹAĺćĚĚA[xgĺđLqˇé\˘Í{żIÉžmť¨ćŃPťłęASIČĘĚŮĆńÇŞ1940NÜĹÉŘžłę˝B
ÂĂ
168:PRQlÚĚfłń
21/10/01 16:43:25.67 9nXmqzo6.net
>>167
ÂĂŤ
ąĚĘĚăÉÍAQRzW[ĚžtđgÁ˝čŽťŞČłęAťęŞ˝˘ăŠĚ_wŇŞŢĚ_đwÔŰĚWĆČÁ˝ŞARzW[đp˘éű@Ěď_ĚęÂÍAťęŞ ÜčďĚIĹȢąĆĹ éBxihEh[NAWEeCgA~bVFEn[EBPÉćéÇ_ÖĚvŁA¨ćŃQEmCLqÉćéǨćŃĺć_ĚÄđßĚĘĆľÄA é˘Í˝ĚwŇÉć鞌IČÝöŽÉÖˇéĆŃĆÖAľÄA1990NăÉÍRzW[đp˘Č˘ńíÉžmČŢĚ_Ě\ťŞm§łę˝BąĚ ˝čĚÚ×ÍAáŚÎmCLqĚ{đQĆšćB
URLŘݸ(ja.wikipedia.org)
ŢĚ_ĚŘĚśÝč (Takagi existence theorem) ĆÍAăĚ K ÉξĝĚLŔA[xgĺĆ K ĚęĘťłę˝CfAŢQĚÔÉ 1 Î 1 ĚÎŞśÝˇéƢ¤čĹ éB
ąĚčđśÝčĆÄÔRÍAŘžĚĹŕ˘ďČŞŞ K ĚA[xgĺĚĚśÝđŚˇŞÉ éŠçĹ éB
(řpIč)
Čă
169:PRQlÚĚfłń
21/10/01 17:06:10.64 9nXmqzo6.net
>>48 âŤ
>URLŘݸ(www.math.titech.ac.jp)
>ŢĚ_ cű YęY
(řpJn)
P2
ŢĚ_ĚpĆľÄ
Kronecker ĚÂt̲. ńĚĚCÓĚLŔA[xgĺÍCM
Č~ČüĚj sĎĘĚlĆŞ_ĚŔWđYÁľÄžçęéB
Şđľ˝(ąęÍKronecker-Weber ĚčĚńĚÖĚgŁĹ é)B
(řpIč)
hCM Č~ČühÍAć@iCMjđÂČ~Čü̹ƚË
śÉྪȢĚĹAâŤĹˇ
URLŘݸ(en.wikipedia.org)
In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers;[1] and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense (it roughly means that the action on the tangent space at the identity element of A is a direct sum of one-dimensional modules). Put another way, it contains the theory of elliptic functions with extra symmetries, such as are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice.
ÂĂ
170:PRQlÚĚfłń
21/10/01 17:06:42.85 9nXmqzo6.net
>>169
ÂĂŤ
URLŘݸ(ja.wikipedia.org)
ć@(complex multiplication)ĆÍAĘíćčŕĺŤČÎĚŤđŕÂČ~ČüĚ_ĚąĆđ˘¤BĘ̢˘Š˝đˇęÎAüúiqipęĹj(period lattice)ŞKEXŽĚiqĹ Á˝čAAC[V
^CŽĚiqĹ Á˝čˇéć¤ČA]čČÎĚŤđÂČ~Ě_Ĺ éBČ~ČüĚłťĹ éA[x˝lĚÉ¢ÄŕŻlÉĺŤČÎĚŤđŕÂęŞ čAąęçđľ¤ĚŞć@_Ĺ éB
ÁęÖĚ_ĆľÄAťĚć¤ČČ~â˝ĎĄfđÍĚA[xÍAĺŤČÎĚŤđŕ¹ƊçťĚÖŞ˝ĚŽđÝ˝ˇąĆŞ˘ŚéBÁĘČ_ĹÍďĚIÉvZÂ\ČÁęlđÂBÜ˝ć@ÍăIŽ_ĚSIČe[}Ĺ čA~ŞĚĚ_đćčLgŁˇéđÂ\ɡéB
ć@ÍAńĚĚŢĚɨŻéÝ@ĽAĺCfAčAŞňĚlqđAČ~âČ~ČüĚąĆÎĹďĚIÉŤ\ˇąĆđÂ\ơéB_tBbgEqxgÍAČ~ČüĚć@_ÍwĚÝČç¸Aˇ×ÄĚČwĚĚĹŕüľ˘ŞěĹ éĆžÁĢé[1]B
URLŘݸ(ja.wikipedia.org)
CM-^CvĚA[x˝lĚ
Ě K ăč`łę˝A[x˝lĚ A ŞCM-^Cv(CM-type)Ĺ éĆÍAŠČŻ^ End(A) ĚĹ\ŞÉĺŤČŞÂˇÂđÂąĆđ˘¤BąĚpęÍć@ (complex multiplication) _ŠçĢÄAć@_Í19˘IÉČ~Čṳ̈̽ßJłę˝B20˘IĚăIŽ_Ćăô˝wĚĺvČŹĘĚĐĆÂÉAA[x˝lĚĚł d > 1 Ě_Ěłľ˘čŽťŞŠłę˝ąĆŞ éBąĚâčÍA˝ĎĄf_đg¤ąĆŞńíɢďĹ é˝ßAńíÉŰIĹ éB
ÂĂ
171:PRQlÚĚfłń
21/10/01 17:07:14.75 9nXmqzo6.net
>>170
ÂĂŤ
tH[}Čč`ÍALĚ Q Ć End(A) Ěe\Ď
{\displaystyle \mathrm {End} _{\mathbb {Q} }(A)}{\displaystyle \mathrm {End} _{\mathbb {Q} }(A)}
Í Z ăAł 2d Ě¡ŞÂđÜńŢéąĆĹ éBd = 1 ĚĆŤAąĚąĆÍńĚČOÉÍ čŚČAEnd(A) ÍńĚĚŽÂipęĹj(order)Ĺ éBd > 1 ÉÎľÄÍAŔĚĚńgĺĹ éCMĚĚęŞärˇ×ŤÉÎŰĹ éBA ŞPA[x˝lĚĹÍȢŠŕľęȢiáŚÎAČ~ČüĚJeVAĎjąĆđ˝fˇéźĚźĚęŕ éBCM-^CvĚA[x˝lĚĚĘĚźĚÍA\ŞÉ˝Ěć@đÂA[x˝lĚĹ éB
K ŞĄfĚĹ ęÎACÓĚCM-^CvĚ A ÍAŔÍAĚĹ éč`ĚipęĹj(field of definition)đÁĢéBŠČŻ^ÂĚÂ\Č^CvÍAÎiT`ĚÎipęĹj(Rosati involution)jđŕÂÂĆľÄůÉŞŢłęĢÄACM-^CvĚA[x˝lĚĚŞŢđąŤoˇBČ~ČüĆŻść¤Čű@ĹCM-^CvĚ˝lĚđ\ŹˇéÉÍACd ĚĚiq Š ŠçnßAA[x˝lĚĚ[}ĚÖWŽđlŚÉüęéKvŞ éB
CM-^Cv(CM-type)ÍAPʳɨŻé A ĚłĽÚóÔăĚAEndQ(A) ĚiÉĺj¡ŞÂ L ĚěpđLqľ˝ŕĚĹ éBPČíŢĚXyNg_ŞKłęAL ŞĹLxNgĚîęđĘľÄěpˇéąĆ𦷱ƪūéBž˘ˇŚéĆAL Í A ĚłĽxNgęĚăĚÎpsńđĘľ˝ěpđÁĢéBL ŠĚŞĄĚĚĚĎĹÍČĚĹ éƢ¤PČęÉÍACM-^CvÍ L ĚĄfßÝ(complex embedding)ĚXgĹ éBĄf¤đđyAĆľÄA2d ÂĚĄfßÝŞ čACM-^CvÍeXĚyAĚŠçęÂđIđˇéBťĚć¤ČCM-^CvĚSÄŞŔťłęéąĆŞmçęĢéB
uşÜYĆJRLĚî{IĘÍACM-^CvĆwbPĚL-ĚąĆÎĹAA ĚnbZEFCĚL-đvZˇéąĆŞĹŤAąęŠçąołę˝łŔŞđÂBąęçŞAČ~ČüĚęĚ}bNXEhCOipęĹj(Max Deuring)ĚĘđęĘťˇéB
(řpIč)
Čă
172:PRQlÚĚfłń
21/10/01 17:23:08.14 9nXmqzo6.net
>>169 âŤ
şL uŢĚ_đąŚÄv ŞŞŠčŐŠÁ˝
uwZ~i[v1967N8 ĚLžť¤Ĺˇ
URLŘݸ(www.nippyo.co.jp)
hNgEN[K[ĚwuŔ1 vę@šY 1992.08
ć2@ŢĚ_đąŚÄ
@@@@ LŔĚĚb
@@@@˛Ą\zĚąĆ
@@@@ŢĚ_đąŚÄ
URLŘݸ(ja.wikipedia.org)
vę šYiŞ Ýż¨A1928N - 1990N213újÍAú{ogĚwŇĹ éB
1960NÉĺwĹmđćžľ˝[1]B
Ţ̤ÍAsG[ElEh[j
ÉćéFC\zĚŘž(Deligne 1974)ŠçŞIÉą}kW\zĚŘžÉÂČŞÁ˝B
1966NAŢÍvęt@Co[˝lĚipęĹjđąüľ˝[2]B
ŢĚwKA̲\Q_Ć÷ŞűöŽxÍAKA_ĚĎ_Šçí˘óÔâtbNX^÷ŞűöŽČÇĚgsbNđl@ľ˝AwwśĚ˝ßĚQ_Ć÷ŞűöŽÉÖˇéęAĚu`Ĺ éB
(řpIč)
Čă
173:PRQlÚĚfłń
21/10/01 17:26:03.83 9nXmqzo6.net
>>172 ÖAîń
EpwiÜŢKA_j9
˝ÚŘݸ(mathÂ:166Ô)
>ąąĚŢĚ_ĚđŕŞAuşÜYĚuć@üĺv wĚ äÝ 7Ş2
>işLĹ3ŞŞ1955NžŠçA7ŞžĆ1959Nžë¤j
ąęĚćŞ Á˝işLj
huşÜY qivęšYE´
BY LjCuć@üĺvCwĚŕÝ 5Ş1h1957 Şłľť¤ŠČ
é˘ÍA7Ş2ɹҪ éĚŠH@şLĚěűYćśĚĆąëÉÍA7Ş2ÍšBcO
iQlj
URLŘݸ(twitpic.com)
ć
uşÜY qivęšYE´
BY LjCuć@üĺvCwĚŕÝ 5Ş1CVwlWciSSSjŇWEwĚŕݧsďC1957Cpp.65-73.
URLŘݸ(www.ms.u-tokyo.ac.jp)
ěűYĚdÔfŚÂ
(C1) wĚŕÝ
ąĚżÍAťĚĚuę_ń未HĺđŢŻłęéĆŤÉAMdČżČĚĹ ĚÄéÉEŃȢAƢ¤ąĆŸ˘Ä¨˘˝ŕĚšBŞ˝sŽSČ ŕĚšŞAťĄ[˘ŕĚŞ čܡB
@ßÉ uÚi\WjvđQơéąĆ𨡡߾ܡB
A@ÖESwAď@ÖEwĚŕÝB
URLŘݸ(www.ms.u-tokyo.ac.jp)
wĚŕÝ
ßÉ ``Úi\Wj'' đŠéąĆđ¨E߾ܡB
URLŘݸ(www.ms.u-tokyo.ac.jp)
Úi\Wj
(řpIč)
Čă
174:PRQlÚĚfłń
21/10/02 16:46:35.10 tWmCJmdX.net
~żWŚ
żŢ
>>1
Í[ń´[˘ľáIÍ[ń´[˘ľáIÍ[ń´[˘ľáIÍ[ń´[˘ľáI˘ÂŠńˇéĚH
175:PRQlÚĚfłń
21/10/02 17:34:07.69 X8Zxjdm/.net
>>174
Čńž˘A¨TŠ
wpśŁĹsĚeLXgÉÍAżiŞ ÁÄAě ŕ é
łżöJwpśŁÉŕAŕżëńě Í éŞ
oT𞌾ĢéČăAŢĹÍ čÜšńişLj
URLŘݸ(news.yahoo.co.jp)
RsyEăsĹĎÜť¤ĆľÄ˘éwśłńÖFřpE]ÚEŢĆÍEťĚá˘ĆÍFě @ĆśU˘
Oä^jVÂËĺwĺw@ Ő°Sw¤Č łöiĐďSwj
2014/3/22(y) 15:31
Ą ¤_śA¤|[gɨŻéřpĆÍ
¤_śi¤|[gjɨ˘ÄuřpvĆÄÎęéŕĚĚ˝ÍA¤ŕeĚĐîĹľĺ¤B˝ĆŚÎAuOäi2022jÍIWW
[XŞA`GCWOÉřĘŞ éąĆ𦵽vƢÁ˝ďÉOä̤ŕeđ˘ÄAĹăÉuřpśŁvĆľÄoTđŤÜˇËB
ÇńÇńřpľÄžł˘BBÍAwâĚćyĹ él̨ɧÁĤđißܡBĺćśĚ¤ŕAĹßĚVľ˘¤ŕ˝łńÇÝAřpľÄžł˘BřpłęéűŕAź_ČąĆĹ čA˝řpłęéąĆÍ]żÉÂČŞčܡĚĹAĺ˝}šB
ąęÉÎľÄA˘ÔĹćžíęéřpÍAčĚžtâśÍđťĚÜÜÄfÚˇéąĆšB˝ĆŚÎAuOäÍ2034NĚAďɨ˘ÄwéLqąťŞlŢđ~¤BęĚó]Ĺ éxĆq×ĢévƢÁ˝ďšB¤_śĹŕANŠĚžtAśÍđAťĚÜÜřpˇéąĆŕ éĹľĺ¤B
176:PRQlÚĚfłń
21/10/02 23:08:18.29 tWmCJmdX.net
cOČŞçŢšB˝ĚČç¨OÉŠoÍȢžë¤ŻęÇ~X[hÉŤpľÄéŠçĄ
Ü[˝Nđ|jÎƨᢾ˝ČZXł˘ČBŞŕŤ˘AĚÉußęéAZXł˘AĐăŠBúçłpśá̤Ą
177:PRQlÚĚfłń
21/10/03 06:48:20.41 gtH9cx8i.net
>>176
Ü[˝Nđ|jÎƨᢾ˝Č
¤ńH@źŽĚ¨ÁłńŠ˘H
178:PRQlÚĚfłń
21/10/06 11:49:16.61 6qp+V25O.net
URLŘݸ(books.j-cast.com)
books.j-cast
uABC\zvŞwĚwďÉfÚłęȢR
2020/3/18 i@XiŹj
đÖĚšŘđŚˇ
@fĚĎđߎÁÄÍAąńȹƪžŚéŠŕľęȢBÂÜčAŠRĚč`žB1É1đŤľÄ˘ÁÄěçę˝ŕ̞ơéuyAmĚövŞćmçęéBŤľZÉćéč`žBęűAŠŻZĹŕč`ĹŤéBŠR͡×ÄfĚĎÉŞđĹŤéĚĹAťęđˇ×ÄěÁÄŹł˘ÉŔ×éű@ži˝žľ1ÍfĚ0ćjBđťńČӤɊéĆAŤľZĆŠŻZÍƧľÄ˘ÄŞŁĹŤéŠŕľęȢĆvŚÄéB
@ÁĄłńĚŕžđ~˘EńĹIUT_đĐîˇéĆą¤žB
@EŮČéwĚäiIUT_ĹÍuniversesAÁĄłńĚägĹÍAŤľZAŠŻZŞŘ裳ęÄŠŻZžŻđLŃkÝłš˝˘EjđÝčBťŔ˘EÉvZŇŞ˘ÄAťąÉerŞ ÁÄćĘĚÉŻśvZŇŞ˘éB˝žľQÂĚvZŇÍŻśžŞ|Żçęé§ńŞŮČÁĢé\Ƣ¤Ó¤ÉäÍťŔ˘EŕÜßÄüęqŽÉČÁĢé
@EvZĚQ_IÎĚŤivZű@ĚVsjđAevZŇÉvZĚÎŰâvZű@đ`B
@EóMľ˝ÎĚŤđîÉAťęźęĚäĹłĚvZĚÎŰâvZű@đłBvZđŔsˇé
@EÎĚŤĚĘMâłĹśśésčŤEиÝAÂÜčvZĘĚTCYĚá˘đčĘIÉ]żľÄsŽđą
wÉÍBłŕ é
@ĹÍABC\zÍǤŠB\zĚĺŁĹ éuc ?dOi1{ĂjvBąęĚIUT_ĹĚudeg Ś
deg q{cvÖĚAđÚwˇB
@]ŇĚć¤ČśnogŇÉudeg vÍłžÁ˝ŞAifOjđ\ˇLžBąąĹÍdeg ŚifOEe[^jŞťŔäĹĚvZĘAdeg qÍŠŻZđLkłš˝äĹĚvZĘĆČéBEÓÉÁŚçęĢécÍAABC\zĚcĆÍʨĹAиÝĚčĘI]żĹßç꽏łČlžBIUT_ÉćéABC\zÍAťŔäĹĚÝćŞAŠŻZLkäĹĚÝććčଳ˘ąĆÉAłš˝˘óžB
ÂĂ
179:PRQlÚĚfłń
21/10/06 11:49:39.98 6qp+V25O.net
>>178
ÂĂŤ
@˘ć˘ć{_BÁĄłńÍąąĹAąęÜĹuŠŻZđLŃkÝłš˝ävĆÄńŢ˝ŕĚđŚˇBťĚäĆÍAťŔäĚuqvđLkäĹĚuqĚćvÉÎłš˝ŕĚžBąęÍLogđp˘éĆAum Log ŕLog viźđÔĚÍßĹ éąĆÉÓjĆ\łęéBLogiŻ˝jĆćÉoÄŤ˝degĚá˘ÍAąąĹĚđĚăĹÍlŚČÄ條¤žBŻść¤ČŕĚĆlŚÄ˘˘B
@ŽĚŹęĹ\ˇĆAą¤ČéB
m Log Log {cim Log ŕLog žŠçAłĚlđÁŚéĆuvÉČéj
¨deg Ś
deg q{c
¨deg qÍŹł˘AÂÜčc ? dOi1{ĂjĚĂÍŹł˘
ĆČÁÄ؞͎ŹˇéAƢ¤B
@2020N43úÇL@wĚ´ďâƢíęéuABC\zvđsĺwđͤĚ]Vęłöi51jŞŘžľ˝Ćłęé_śŞA¢ÉŰIČwÉfÚłęéąĆÉČÁ˝BsĺŞ2020N43úÉ\ľ˝B
(řpIč)
Čă
180:PRQlÚĚfłń
21/10/06 11:59:08.55 6qp+V25O.net
>>178-179 âŤ
iřpJnj
@EŮČéwĚäiIUT_ĹÍuniversesAÁĄłńĚägĹÍAŤľZAŠŻZŞŘ裳ęÄŠŻZžŻđLŃkÝłš˝˘EjđÝčBťŔ˘EÉvZŇŞ˘ÄAťąÉerŞ ÁÄćĘĚÉŻśvZŇŞ˘éB˝žľQÂĚvZŇÍŻśžŞ|Żçęé§ńŞŮČÁĢé\Ƣ¤Ó¤ÉäÍťŔ˘EŕÜßÄüęqŽÉČÁĢé
@EvZĚQ_IÎĚŤivZű@ĚVsjđAevZŇÉvZĚÎŰâvZű@đ`B
@EóMľ˝ÎĚŤđîÉAťęźęĚäĹłĚvZĚÎŰâvZű@đłBvZđŔsˇé
@EÎĚŤĚĘMâłĹśśésčŤEиÝAÂÜčvZĘĚTCYĚá˘đčĘIÉ]żľÄsŽđą
(řpIč)
ČéŮÇ
iřpJnj
@ĹÍABC\zÍǤŠB\zĚĺŁĹ éuc ?dOi1{ĂjvBąęĚIUT_ĹĚudeg Ś
deg q{cvÖĚAđÚwˇB
ąąĹÍdeg ŚifOEe[^jŞťŔäĹĚvZĘAdeg qÍŠŻZđLkłš˝äĹĚvZĘĆČéBEÓÉÁŚçęĢécÍAABC\zĚcĆÍʨĹAиÝĚčĘI]żĹßç꽏łČlžBIUT_ÉćéABC\zÍAťŔäĹĚÝćŞAŠŻZLkäĹĚÝććčଳ˘ąĆÉAłš˝˘óžB
@˘ć˘ć{_BÁĄłńÍąąĹAąęÜĹuŠŻZđLŃkÝłš˝ävĆÄńŢ˝ŕĚđŚˇBťĚäĆÍAťŔäĚuqvđLkäĹĚuqĚćvÉÎłš˝ŕĚžBąęÍLogđp˘éĆAum Log ŕLog viźđÔĚÍßĹ éąĆÉÓjĆ\łęéBLogiŻ˝jĆćÉoÄŤ˝degĚá˘ÍAąąĹĚđĚăĹÍlŚČÄ條¤žBŻść¤ČŕĚĆlŚÄ˘˘B
@ŽĚŹęĹ\ˇĆAą¤ČéB
m Log Log {cim Log ŕLog žŠçAłĚlđÁŚéĆuvÉČéj
¨deg Ś
deg q{c
¨deg qÍŹł˘AÂÜčc ? dOi1{ĂjĚĂÍŹł˘
ĆČÁÄ؞͎ŹˇéAƢ¤B
(řpIč)
Ö[
181:PRQlÚĚfłń
21/10/06 12:07:25.52 6qp+V25O.net
ąę˘˘Ë
URLŘݸ(jbpress.ismedia.jp)
JBpress (WFCr[vX)
´ďđČuFŰ^Cq~
[_vÉ´Ž
HONZÁI{wFĆFđÂČŽwx
2019.6.4iÎj
đjăĚVË˝żđÍéŠÉ˝í
@]ŇŠgŞwĚflČĚĹfžÍōȢŞA]łöÍąęÜĹđjăÉoęľ˝XĚVË˝żđÍéŠÉ˝íľÄ˘éB
uŤľZĆ|ŻZ𪣡év
uFŰ^Cq~
[_vÉ¢ÄÍARA]ŇÉŕžĹŤéć¤ČxĚŕĚĹÍȢ̞ŞAńíÉČÉž¤ĆAuŤľZĆ|ŻZ𪣡évƢ¤ąĆ羢BाˇŕžˇéĆAŠRĚŤľZĆ|ŻZŠçČéuÂvĆÄÎęéĄGČ\˘đľ˝wIÎŰÉÎľÄAťĚuńÂĚŠRxłvđřŤŁľÄđĚľAđ̡éOĚŤľZĆ|ŻZĚĄGČÜč˘űĚĺ§Á˝Ťżđź´IɨŚâˇČéć¤ÉgݧğˇwIuĚć¤ČŕĚžť¤žB
@ąęžŻĹÍâÍč˝ĚąĆŠŞŠçȢĆv¤ĚĹAŤľZĆ|ŻZĚÖWŤÉ¢ľžŻŕžˇéĆAu1đXÉŤľÄ˘vąĆĹĹŤé1A2A3EEEƢ¤uŤľZIČvŠR̨ŚűžŻĹÍAŠRĚu|ŻZI¤ĘvŞSb\˛ŻżÄľÜÁĢé˝ßAáŚÎAfƢ¤ŕĚĚŤżđcŹľ˝čAfŞťęép^[đLqľ˝čˇéąĆÍōȢ羢B
fÉ¢ÄÍAťęŞńâ{Ƣ¤TOđp˘Äč`łęéąĆŠçઊéć¤ÉAˇŽęÄ|ŻZIČTOĹ é˝ßÉAfŞÇĚć¤Č^C~OĹťęé̊ƢÁ˝âčÍAŤľZĆ|ŻZ̢ŃÂŤđęńfżŘÁÄAťĚăĹĄ éw̢EĆÄÚąľČŻęÎđōȢƢ¤ĚžB
182:PRQlÚĚfłń
21/10/12 21:05:31.64 kAX38bAL.net
ąę˘˘Ë
URLŘݸ(www.maths.nottingham.ac.uk)
News - Ivan Fesenko
Higher adelic theory, talk at Como school on Unifying Themes in Geometry, September 2021
URLŘݸ(www.maths.nottingham.ac.uk)
Higher adelic theory
Ivan Fesenko
Como School, September 27 2021
1 CFT and its generalisations
2 Back to the root: CFT
3 Back to the root: CFT
4 CFT mechanism
5 CFT mechanism
6 Anabelian geometry
7 ePre-Takagif LC
8 2D objects of HAT
9 HCFT
10 Zeta functions
11 Classical 1D theory of Iwasawa and Tate
12 HAT and elliptic curves
13 Measure and integration on 2D local fields
14 Two adelic structures in dimension 2
15 The triangle diagrammes
16 Higher zeta integral
17 HAT and meromorphic continuation and FE of the zeta function
18 HAT and GRH
19 HAT and the Tate?BSD conjecture
P29
Anabelian geometry and IUT
P33
Powerful restoration results in absolute mono-anabelian geometry were established by Mochizuki
and applied in the IUT theory.
183:PRQlÚĚfłń
21/10/12 23:04:19.12 kAX38bAL.net
ąę˘˘Ë
URLŘݸ(www.kurims.kyoto-u.ac.jp)
Ż TęY u
URLŘݸ(www.kurims.kyoto-u.ac.jp)
ĚĚPA[xIł (uXCh),
FŰ^Cq~
[[_ĚŘĆXČéW,
sĺwđͤ,
2015.3.9-2015.3.20.
Mono-anabelian Reconstruction of
Number Fields
Yuichiro Hoshi
RIMS
2015/03/09
Contents
1 Main Result
2 Two Keywords Related to IUT
3 Review of the Local Theory
4 Reconstruction of Global Cyclotomes
184:PRQlÚĚfłń
21/11/13 23:13:31.45 OtqEOAj/.net
URLŘݸ(www.math.titech.ac.jp)(2013)/Graduate/Special_Lectures_on_Mathematics_B_I.html
u`ź wÁĘu`aćęiSpecial Lectures on Mathematics B Ij
Juwú@Owú PĘ 2--0--0
S@Ż@TęY@ńíÎutisĺwđͤ@utj
yu`ĚÚIz
@A[xô˝wĆÍCuA[x˝lĚƢ¤ éÁĘČNXÉŽˇéă˝lĚÍC
ťĚ_Iî{QĚQ_IČŤżÉćÁÄťĚ_ô˝wIŤżŞŽSÉčłęéĹ ë¤v
Ƣ¤\ŞÉîâÄC1980 NăÉ Grothendieck Ƣ¤wŇÉćÁÄńĽłę˝_ô˝wĚęŞěšD
ąĚu`ĹÍCťĚA[xô˝wÖĚüĺđÚIĆľÄCp iÇĚi= p iĚĚLŔgĺĚjÉΡé
é Grothendieck \z^ĚĘip iÇĚŞťĚâÎ Galois QĆ étÁîńŠçłĹŤéƢ¤ĘjĚ
đŕđs˘ÜˇD
yu`vćz
1. A[xô˝wĆÍ
2. p iÇĚĆťĚâÎ Galois Q
3. ÇŢĚ_EHodge-Tate \ť
4. ł (1)
5. ł (2)
ÂĂ
185:PRQlÚĚfłń
21/11/13 23:13:59.64 OtqEOAj/.net
>>184
ÂĂŤ
yłČEQlz
@A[xô˝wĚüĺIČđŕĆľÄC
Eşş, ĘěŔRj, ]Vę, ăČüĚî{QÉÖˇé Grothendieck \z, w, 50 (1998), 113-129.
đ°ÜˇDÇĚCÇŢĚ_CHodge-Tate \ťÉ¢ÄĚQlĆľÄC
EJ.-P. Serre, Local fields, Translated from the French by Marvin Jay Greenberg. Graduate Texts in Mathematics,
67. Springer-Verlag, New York-Berlin, 1979.
EJ.-P. Serre, Local class field theory, 1967 Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965)
pp. 128-161 Thompson, Washington, D.C.
EJ.-P. Serre, Abelian l-adic representations and elliptic curves, McGill University lecture notes written with
the collaboration of Willem Kuyk and John Labute W. A. Benjamin, Inc., New York-Amsterdam 1968.
đťęźę°ÜˇDÜ˝CąĚu`ĹťĚŕžđÚWƾĢéčÍC
E]Vę, A version of the Grothendieck conjecture for p-adic local fields, Internat. J. Math. 8 (1997), no. 4, 499-506.
E]Vę, Topics in absolute anabelian geometry I: generalities, J. Math. Sci. Univ. Tokyo 19 (2012), no. 2, 139-242.
EŻTęY, A note on the geometricity of open homomorphisms between the absolute Galois groups of p-adic local fields,
to appear in Kodai Math. J.
É čܡD
186:PRQlÚĚfłń
21/11/26 18:02:35.84 3Zp5TRQm.net
şLhIntroducing anabelian geometry, a general talkh IVAN FESENKO
ąęA\˘˘Ë
URLŘݸ(ivanfesenko.org)
IVAN FESENKO
Research ? Ivan Fesenko
L Anabelian geometry and IUT theory of Shinichi Mochizuki, and applications
Introducing anabelian geometry, a general talk
URLŘݸ(ivanfesenko.org)
Introducing anabelian geometry
Ivan Fesenko
187:PRQlÚĚfłń
21/12/05 18:19:17.01 e0gyQODW.net
URLŘݸ(people.math.rochester.edu)
Saul Lubkin
Professor of Mathematics
URLŘݸ(en.wikipedia.org)
Jean-Louis Verdier (French: [v??dje]; 2 February 1935 ? 25 August 1989) was a French mathematician who worked, under the guidance of his doctoral advisor Alexander Grothendieck, on derived categories and Verdier duality. He was a close collaborator of Grothendieck, notably contributing to SGA 4 his theory of hypercovers and anticipating the later development of etale homotopy by Michael Artin and Barry Mazur, following a suggestion he attributed to Pierre Cartier. Saul Lubkin's related theory of rigid hypercovers was later taken up by Eric Friedlander in his definition of the etale topological type.
188:PRQlÚĚfłń
21/12/10 10:08:46.26 ZfXXklGr.net
_ô˝wĆăô˝wĚá˘ÁÄČńšŠH
˝ÚŘݸ(mathÂ:104Ô)
104 źOFPRQlÚĚfłń[sage] eúF2021/10/23(y) 15:02:26.36 ID:bV1+EpOI
˘ÂĚÔÉâçApizbW_Ěú{ęĹwikipediaŞoĢ˝
URLŘݸ(ja.m.wikipedia.org)
˘Üâ_ô˝ÉKvsÂČTOžľ 誽˘Č
(řpIč)
¢Ĺ
URLŘݸ(ja.wikipedia.org)
pizbW_
URLŘݸ(en.wikipedia.org)
p-adic Hodge theory
189:PRQlÚĚfłń
21/12/21 14:47:01.98 H4QZamD3.net
Inter-universal geometry ĆABC \z47
˝ÚŘݸ(mathÂ:44Ô)
44 źOFPRQlÚĚfłń[] eúF2021/12/21(Î) 10:31:51.78 ID:ATxzruO4
Fesenko̎抽ŻÇAIUTÉ¢ÄŕbľÄé
URLŘݸ(m.youtube.com)
RIMSĚIUTT~bgĹĚuŕeĆŮÚę
190:PRQlÚĚfłń
22/01/02 09:38:15.90 DhlSCn4I.net
hßĆťÝ̤Ěń (2008-03-25 ťÝjh
ąęÍA\dvČśŁžË
ąąÉAIUTĚ\zŞŚłęĢé
URLŘݸ(www.kurims.kyoto-u.ac.jp)
] ßĆťÝĚ
URLŘݸ(www.kurims.kyoto-u.ac.jp)
EßĆťÝ̤Ěń (2008-03-25 ťÝj
úĚŕÝ
wĘđćžľ˝ 1992 NÄŠç 2000 NÄÜĹĚ̤ĚĺČe[}ÍĚOÂ
ɪޡéąĆŞĹŤÜˇF
(a) p i TeichmNuller _F(1993 N`1996 N)
ąĚ_ÍAĄfĚăĚoČI[}ĘÉΡé Koebe Ěăź˝ĘÉ
ćéęÓťâAťĚW
CÉΡé Bers ĚęÓťĚ p iIČŢĆŠé
ąĆŕĹŤAÜ˝ Serre-Tate ĚĘíA[x˝lĚÉΡéWŔWĚ_Ě
oČČüĹĆŠéąĆŕĹŤéBÚľÍA
A Theory of Ordinary p-adic Curves
â
An Introduction to p-adic TeichmNuller Theory
đ˛QĆşł˘B@
(b) p iA[xô˝F(1995 N`1996 N)
ąĚ_Ěă\IČčÍAuň p iĚvi p iÇĚăLŔśŹČĚĚ
ŞĚjăĚÎIČÝčɨ˘ÄAoČIČüÖĚCÓĚ˝lĚŠçĚńč
IČËĆAťęźęĚ_Iî{QĚÔĚJOŻ^ĚÔÉŠRČSPËŞś
ݡéƢ¤ŕĚĹ éBÚľÍA@
The Local Pro-p Anabelian Geometry of Curves
đ˛QĆşł˘B
(c) Č~ČüĚ Hodge-Arakelov _F(1998 N`2000 N)
ąĚ_ĚÚWÍAĄfĚâ p iĚăĹmçęĢé Hodge _ĚŢ
đAĚăĚČ~ČüÉÎľÄ Arakelov _IČÝčĹŔťˇéąĆÉ éB
ă\IČčÍAĚăĚČ~ČüĚŐgĺăĚ éíĚÖóÔĆAČ~
ČüĚŞ_ăĚÖŠçČéóÔĚÔĚAĚ̡×ÄĚf_ɨ˘ÄvĘ
Ći éëˇđ˘Äjź§IČSPËđ壡éŕĚĹ éBąĚ_ÍA
ĂTIČKEXĎŞ
ç ? e?x2dx = ăÎ
ĚuŁUIXL[_ĹvĆŠéąĆŕĹŤéBÚľÍA@
A Survey of the Hodge-Arakelov Theory of Elliptic Curves I, II
đ˛QĆşł˘B
ÂĂ
191:PRQlÚĚfłń
22/01/02 09:38:56.87 DhlSCn4I.net
>>190
ÂĂŤ
V˝ČggÖĚš
Hodge-Arakelov _ĹÍA_IČ Kodaira-Spencer ËŞ\ŹłęéČÇA
ABC \zĆĚÖAŤđşßŠˇć¤ČŁÍIȤʪ éŞAťĚÜÜuABC \
zĚŘžvÉpˇéÉÍAŞ{IČáQŞ čs\ŞĹ éBąĚć¤ČáQđ
ˇé˝ßÉÍA
ĘíĚ_ô˝ĚXL[_IČggđ´zľ˝gg
ŞKvĹ ë¤ĆĚź´ĚşA2000 NÄŠç 2006 NÄÉ|ŻÄAťĚć¤Čggđ
\zˇé˝ßÉÍ˝ŞKvŠÍőľnßAÜ˝ťĚggĚyäĆČélXČwIC
tĚŽőÉ
čľ˝BąĚć¤Č¤ŽđxŚ˝î{OÍAĚć¤Čŕ
ĚĹ éF@
ڡ׍ÎŰÍAÁčĚ_ô˝IÝčÉoęˇéÂXĚXL[ĹÍČ
AťęçĚXL[đ§ˇéŰIČgš_Ip^[ȢľÍťĚp
^[đLqľ˝gš_IASYĹ éB@
ąĚć¤ČlŚűđîÉľ˝ô˝ĚąĆđAuFŰiInter-universal=IUjô
˝vĆÄÔąĆÉľ˝BOŞÉ¨˘Ä˘˝ťŰĚĹŕî{IČáĆľÄĚOÂŞ
°çęéF
EOEXL[Ěô˝É¨ŻémCh
EA[xô˝É¨Żé_Iî{QKA
EŢťČŔčČüĚoÎOtAŰIČOtĚ\˘
ąĚOÂĚáÉoÄéumChvAuKAvAuOtvÍA˘¸ęŕAuv
Ƣ¤TOĚÁĘČęÉ˝éŕĚĆŠéąĆŞĹŤéBiáŚÎAOtĚęA
OtăĚpXđlŚéąĆÉćÁÄŞĹŤéBj]ÁÄAIU ô˝Ěiˇ×ÄĹÍ
ȢŞjdvȤĘĚęÂÍA@
uĚô˝v
Ĺ\łęéƢ¤ąĆÉČéBÁÉAA[xô˝ĚęAąĚuĚô˝vÉÎ
ˇéĚÍA
âÎA[xô˝
iîbĚĚâÎKAQđAłX^Śçę˝ŕĚƾĊôłČ˘ÝčĹĚA[
xô˝jĹ éB
ÂĂ
192:PRQlÚĚfłń
22/01/02 09:41:25.89 DhlSCn4I.net
>>191
ÂĂŤ
ąĚ 6 NÔi 2000 NÄ`2006 NÄjĚA
uĚô˝vââÎA[xô˝
đĺe[}Ćľ˝¤Ěă\IČáĆľÄAĚć¤ČŕĚŞ°çęéF
EThe geometry of anabelioids i2001 Nj
XiCÓĚJŞQĚSŞŠžjČLŔQđô˝IČÎŰƾľ˘A
ťĚLŔG^[í˘ĚĚŤżđ˛×éBÁÉAp iĚăĚoČČüĚ_Iî
{QƾĜśéLŔQĚęAąĚÍAăź˝ĘĚô˝đAzłšéć¤Č
âÎIŠÂWIČuLEŤvAlXČťĄ[˘Ťżđ˝ˇB
EThe absolute anabelian geometry of canonical curves i2001 Nj
p i TeichmNuller _ÉoęˇéWČüÉÎľÄAp iĚăĚŕĚĆľÄĆČ
éâÎA[xô˝^ĚčđŚˇB
ECategorical representation of locally noetherian log schemes i2002 Nj
XL[âOEXL[ŞAťĚăĚLŔ^ĚiOjXL[ĚŠçŠR
ÉłłęéƢ¤A1960 NăÉŠłęÄਊľČ˘î{IČĘđŚˇB
ESemi-graphs of anabelioids i2004 Nj
ĂTIČugraph of groupsv̡üăÉ éusemi-graph of anabelioidsvÉÎ
ľÄAlXČXL[_IČup^[vŞŔÉ˝fłęéąĆâAťęÉÖAľ
˝uA[xô˝vĚĘđŘžˇéB
EA combinatorial version of the Grothendieck conjecture i2004 Nj
ŢťČŔčČüÉtˇéusemi-graph of anabelioidsvđAXL[_ŞžŚI
ÉoęľČ˘AŰIČgš_IggĹćčă°AlXČuA[xô˝vĚ
ułčvđŚˇB
EConformal and quasiconformal categorical representation of hyperbolic Riemann surfaces i2004 Nj
oČI[}ĘĚô˝đńĘčĚAv[`Ĺ_IÉLqˇéBťĚ¤żĚ
ęÂÍAăź˝ĘÉćéęÓťđo_Ćľ˝ŕĚĹAŕ¤ęÂÍA[}ĘăĚ
uˇű`vip\˘ÉÎjâu˝slÓ`vi^p\˘ÉÎjÉćéŕĚĹ éB
ÂĂ
193:PRQlÚĚfłń
22/01/02 09:44:47.36 DhlSCn4I.net
>>192
ÂĂŤ
EAbsolute anabelian cuspidalizations of proper hyperbolic curves i2005Nj
ĹLČoČČüĚ_Iî{QŠçAťĚJŞXL[Ě_Iî{Qđł
ˇé_đWJˇéBąĚ_đALŔĚâ p iĚăĚâÎA[xô˝Ép
ˇéąĆÉćÁÄAlXȢđ\zđđB
EThe geometry of Frobenioids I, II i2005 Nj
KAĚć¤ČuLetale nv\˘ĆAiOEXL[Ě_ÉoÄéj
mChĚć¤ČuFrobenius nv_I\˘ŞAÇĚć¤Éěpľ ˘AÜ˝ÇĚć¤ÉŢĘĹŤéŠđ¤ˇéB
ĚÉΡé TeichmNuller _
2006 NĚ㟊çAÚwˇ×Ť_Ě`Şć¤âĹÜÁÄŤÄAťĚ_đL
qˇé˝ß̡MŽŞ{iIÉnÜÁ˝BąĚ_Ěu`vĆÍAęžĹž¤ĆA
ĐëĘíĹLŠtŤĚłWĚoČČüÉÎľÄWJˇé p i TeichmNuller
_ĆAup^[IÉvŢIČ_đAę_˛ŤČ~ČütŤĚĚÉÎľ
ÄWJˇé@
Ƣ¤ŕeĚŕĚĹ éBöÝÉAąąÉoÄéiĚăĚjuę_˛ŤČ~Čüv
ĚÉAťĚČ~ČüĚăÉWJłęé Hodge-Arakelov _ŞÜÜęĢéBą
Ě_ĚąĆđAuIU TeichmNuller _viuIU TeichvjĆÄÔąĆÉľ˝B
IUTeich ĚűÍA{żIÉXL[_ĚggĚOiuIU IČggvjĹ莝łęé
_Ĺ éÉŕÖíç¸A˛×ęβ×éŮÇ p i TeichmNuller _iupTeichvj
ĆĚ\˘IAup^[IvŢŤŞAÓOĆ׊˘ĆąëÜĹyÔŕĚĹ éąĆ
ÉôxĆČ´ŽđoŚ˝ŕĚĹ éB@@
2006 N`2008 NtĚuIUTeich ĚővÖAĚ_śÍĚlŃĹ éF
ÂĂ
194:PRQlÚĚfłń
22/01/02 09:46:23.12 DhlSCn4I.net
>>193
ÂĂŤ
EThe Letale theta function and its Frobenioid-theoretic manifestations
i2006 Nj
p iÇĚăĚŢťˇéČ~Čüi Tate curvejĚ éí˘Ěăɜݡée[
^ÖÉtˇé Kummer ŢđG^[Ee[^ÖĆÄÔBąĚG^[Ee[
^ÖâAe[^ŠžťÉtˇé Kummer _IČÎŰÍAlXČťĄ[˘âÎ
A[xIČŤżâŤŤżđ˝ľÄ˘éBąęçĚŤżĚęÍ Frobenioid
Ě_ĆĚÖAĹßÄÓ`đÂŕĚÉČéBÜ˝AąĚG^[Ee[^Ö
ÍAIUTeich ĹÍApTeich ɨŻéWI Frobenius żă°ÉΡéÎŰđč
ßé\čĹ éBąĚ Frobenius żă°Ěިđ÷ŞˇéąĆÉćÁÄ ABC \
zĚsŽŞ]¤ĆúҾĢéBąĚć¤ÉľÄsŽđoˇc_ÍA@
ułWĚŽSĚĚ Witt ÂăĚĹLĹçŠČí g ČüĚăÉ Frobenius
żă°Şč`łęĢéĆźčˇéĆAťĚżă°đ÷ŞľÄ÷ŞwĚ
đvZˇéąĆÉćčAsŽ
g ? 1
Ş]¤v
Ƣ¤ĂTIČc_Ě IU ĹĆྦéB
ETopics in absolute anabelian geometry I: generalities i2008 Nj
ąĚV[Yi I,II,IIIjĚĺe[}ÍAâÎA[xô˝đAuGrothendieck
\z^Ě[ŔŤvđÚWĆľ˝_ĹÍČAuQ_IČASY\tgv
ĚJɲŤđu˘˝_ŤˇéƢ¤ŕĚĹ éBąĚćę_śĹÍAlXČ
őIČl@đs¤Bă\IČčĹÍAĘěŔRjÉ`Śˇ˘˝˘oĹĚĘŠ
çAiźjâÎ p iA[xô˝ĹÍĆČé Grothendieck \z^ĚuHom Ĺv
đąBöÝÉAąĚčÍ IUTeich ĆÍźÚÖWĚȢĘĹ éB
ETopics in absolute anabelian geometry II: decomposition groups
i2008 Nj
IUTeich Ě˝ßĚőIČl@ĆĆŕÉAIUTeich ĆÍ_IÉźÚÖWĚȢ
zuóÔĚâÎA[xô˝âA_ĚŞđQŠçîbĚĚÁ@\˘đâÎ p i
A[xô˝IČÝčĹłˇé_đWJˇéB˝žAăŇĚ p iIČ_ĹÍA
ăqĚuFrobenius żă°Ě÷ŞŠçsŽđoˇvc_đp˘Ä¨čANwI
ÉÍ IUTeich ĆÖWˇé¤ĘŞ é
ÂĂ
195:PRQlÚĚfłń
22/01/02 09:46:54.86 DhlSCn4I.net
>>194
ÂĂŤ
ETopics in absolute anabelian geometry III: global reconstruction algorithms i2008 Nj
uGrothendieck \z^Ě[ŔŤvđÚWơéuoA[xô˝vi bianabelian geometryjĆęüđćľ˝uPA[xô˝vi mono-anabelian geometryjđĚăĚĺćIČÝčĹWJˇéB
ąęÍłÉIUTeich Ĺp˘é\čĚA[xô˝
Ĺ éBąĚ_ĚŕeâuIUTeich \zvĆĚÖAŤÉ¢ÄÍA_śĚ Introduction đ˛QĆşł˘B
ąąĹťĄ[˘Ŕđv˘oľÄ¨Ť˝˘Bťŕťŕ Grothendieck ŞLźČ
uFaltings ÖĚčvĹuA[xNwvđńĽľ˝dvČŽ@ĚęÂÍłÉ diophantusô˝ÖĚpĚÂ\ŤÉ Á˝çľ˘B
ÂÜčAA[xô˝ŞiABC \zÖĚpŞúŇłęéjIUTeich ĹSIČđđĘ˝ˇąĆÍAęŠľÄ Grothendieck Ěź´ÉťŽÁ˝WJÉŠóŻçęéB
ÂĂ
196:PRQlÚĚfłń
22/01/02 09:47:42.29 DhlSCn4I.net
>>195
ÂĂŤ
ęűAाuđxđă°ÄvóľđءéĆAťęŮÇPČÖWÉ éíŻĹÍȢąĆŞŞŠéBáŚÎA
Grothendieck ŞzčľÄ˘˝pĚdűĹÍAĚăĚuZNV\zvÉćÁ
ÄĚăĚL_ĚńĚÉŔ𾤹ƪÂ\ÉČéƢ¤Ď@Şc_ĚvĆČéB
ąęĆÍÎĆIÉAuIUTeich \zvĹÍAiĚăĚZNV\zĹÍČj
ĚĆ p iĚĚźűÉξğ§IÉŹ§ˇéiâÎA[xô˝ĚęíĹ
éjPA[xIASYŞĺđđśé
\čĹ éBąĚuPA[xIASYvÍApTeich ɨŻé MFŢ-object
Ě Frobenius sĎĘÉΡéŕĚĹ čAŚż p iĚ_ɨŻé
Witt ÂĚ TeichmNuller ă\łâ pTeich ĚWČü
ĚuIU IިvĆŠéąĆŞĹŤéBĘĚž˘űđˇęÎAąĚuPA[xI
ASYvÍAęíĚWIżă°EŞôđč`ľÄ˘éŕĚĹ éBÜ˝AiP
A[xIČjuKAnvĚÎŰŞ p iĚ_ɨŻé crystali MFŢ-object
Ěş crystaljÉξĢéƢ¤óľÉÍAHodge-Arakelov _ɨŻéu
_I Kodaira-Spencer ËviKAQĚěpÉćéjđAzłšéŕĚŞ éB @
2008 N 4 Šç IUTeich _Ěu{Ěv̡MÉćč|Šé\čĹ éBąĚě
ĆÍA˛ĺGcÉž¤ĆAĚOÂĚ_đ\číšéąĆđĺĚĆľ˝ŕĚĹ éF
ÂĂ
197:PRQlÚĚfłń
22/01/02 09:48:16.96 DhlSCn4I.net
>>196
ÂĂŤ
EThe geometry of Frobenioids I, II
EThe Letale theta function and its Frobenioid-theoretic manifestations
ETopics in absolute anabelian geometry III
öÝÉA2000 NÄÜŤľÄ˘˝XL[_IČ Hodge-Arakelov _ŞKEX
ĎŞ
ç ? e?x2dx = ăÎ
ĚuŁUIXL[_ĹvžĆˇéĆAIUTeich ÍA
ąĚKEXĎŞĚuĺćIKA_ĹȢľÍ IU Ĺv
ĆŠéąĆŞĹŤAÜ˝ĂTIČKEXĎŞĚvZÉoÄéuźđŔWvĆuÉŔ
WvĚÔĚŔWϡÍAiIU ĹĹÍjżĺ¤ÇuThe geometry of Frobenioids I, IIv
Ťľ˝uFrobenius n\˘vĆuLetale n\˘vĚÔĚuär_vÉÎľÄ
˘éĆŠéąĆŞĹŤéBąĚu{ĚvĚ_ÍAťÝĚĆąëńŃĚ_śÉŞŻÄ
\čĹ éB@
EInter-universal TeichmNuller theory I: Hodge-Arakelov-theoretic aspects
i2009 NÉŽŹiHj\čj
p i TeichmNuller _ɨŻéČüâ Frobenius ĚAumod pnvÜĹĚWżă
°ÉΡé IU Ĺđ\ŹˇéB
EInter-universal TeichmNuller theory II: limits and bounds i2010 NÉŽŹiHj\čj
ăLĚumod pnvÜĹĚĎ`Ě n 𮩵Ap iIÉŔÉΡéuIU IČÉ
Ŕv đ\ŹľApTeich ɨŻé Frobenius żă°Ě÷ŞÉΡéŕĚđvZˇéB
(řpIč)
Čă
198:PRQlÚĚfłń
22/01/03 11:20:28.50 M7Pqf1pT.net
ąęǢË
URLŘݸ(www.kurims.kyoto-u.ac.jp)
˝Ź18Nx(ć28ń)wüĺöJuŔeLXg(sĺwđͤCH180731)
KA_ĆťĚW ĘěŔRj
0. ÍśßÉ
KA_ĆÍAEvariste Galois (1811-1832) ÉćÁÄnnłę˝Aă
űöŽĚđĚuˇÉÖˇé_šBťĚî{čÍuĚvĆuQvĆ
˘¤ăwĚî{TOđp˘Äq×éąĆŞĹŤAťÝĹŕŽ_̤
ĚĹĹŕî{IČšďĚPŠ蹯ĢܡB
ąĚu`ĹÍAܸAKA_Ěî{čĚ´śđŠńĹŕç¤
ąĆđÚWÉľ˝˘Ćv˘ÜˇBÉAKA_ĚĂTIÉLźČp
iMVwRĺďâ̤żĚpĚRŞâčƧűĚ{ĎâčĚŰč
IđA é˘ÍATČăĚűöŽĚÁ¸ćĆ׍ŞĚÝđp˘˝đ
ĚöŽĚńśÝĚŘžAČÇjĚŠçčŢđIńĹđŕľ˝˘Ćv˘Ü
ˇBĹăÉAA[xô˝ČÇAťăĚŽ_E_ô˝É¨ŻéK
A_ĚWJÉ¢ÄŕĐîľ˝˘Ćv˘ÜˇB
5. KA_ĚW - łŔKA_ĆA[xô˝
5.1. łŔKA_
ăLĚŻlČđ̢¸ęŠiľ˝ŞÁÄSÄjŞŹ§ˇéAL/K
đKAgĺĆž˘AąĚĆŤAAut(L/K) đ Gal(L/K) ĆLľAL Ě
K ăĚKAQĆÄŃܡBęĘÉÍ Gal(L/K) ÍLŔQÉČčÜšń
ŞAuLŔQvƢ¤ÁĘČíŢĚQÉČčAuĘvŞüÁÄuĘ
QvĆČéąĆŞíŠčܡBąĚęŕAĚć¤ČKAÎŞśÝ
ľÜˇB
URLŘݸ(ja.wikipedia.org)
ËLŔQipę: pro-finite groupj é˘ÍLŔQÍALŔQĚËenĚÉŔÉČÁĢéć¤ČĘQĹ éBKAQâp-iŽđWơéăQČÇA_IÉťĄ[˘lXČQŞËLŔQĚ\˘đÂB
ËLŔQÍŽSsAĹRpNgČnEXhtĘQĆľÄč`łęéBŻlČč`ĆľÄAŁULŔQĚŹˇËenitnjĚËeÉŔitÉŔjƾĞçęéĘQÉŻ^Ĺ éć¤ČQđËLŔQĆčß颤ąĆŕĹŤéB
URLŘݸ(en.wikipedia.org)
Profinite group
(řpIč)
Čă
199:PRQlÚĚfłń
22/02/01 17:50:40.36 Igtg+Ugu.net
tFZRAR[`FErJ[AÉŹf
URLŘݸ(ja.wikipedia.org)
C@EtFZRiIvan Fesenkoj
mŰö
wąwś R[`FErJ[
URLŘݸ(ja.wikipedia.org)
R[`FErJ[ (Caucher Birkar, 1978N - )
2016NAAMSW[i(2010)ɨŻéuÎęĘ^˝lĚÉΡéÉŹfĚśÝvĚ_ś(P. JbV[jiC^AęĹjAC. wRipęĹjAJ. }bJ[iipęĹjĆ̤AĘĚŞśđĆÁÄ[BCHM]Ćžíęé)ÉÎľÄAAMS[AÜipęĹjđöÜľ˝[8]BťľÄ2018NArJ[ÉAut@m˝lĚĚŤEŤĚŘžĆÉŹfvOÖĚvŁvÉÎľÄAtB[YÜŞö^łę˝[9]B
URLŘݸ(www.kurims.kyoto-u.ac.jp)
Website of Masayuki Kawakita
URLŘݸ(www.kurims.kyoto-u.ac.jp)
ÉŹf_ĚW ć32ńwüĺöJuŔ, 31-44 (2010)
ěk^V
ăô˝wĚľ¤ÎŰÍCă˝lĚĆÄÎęéCA§˝ŽĚ¤Ęë_WĆľÄč`ł
ęé}`šDÉŹf_ĆÍCĎϡĹĘč¤ă˝lĚ˝żđ{żIÉŻśŕĚ
ƨŚCeXĚŠçă\IČă˝lĚđoˇé_šDoĚßöĹ˝lĚăĚ]v
ČČüđűkłšéĚšŞCűkÉćÁÄŤ˘ÁŮ_đ½lĚŞśśÜˇDťęđń
łšéěŞtbvĆÄÎęéϡĹCÉŹf_ɨ˘ÄSIČđđĘ˝ľÜˇD
3 łÉŹf_ÍXÉćétbvĚśÝđSĆľÄ 90 NăÉŽŹľÜľ˝ŞCťĚ
łťÍbÍőiKĹľ˝DĆąëŞ 2006 NCrJ[CJbV[jCwCRC}b
J[iÍęĘłĚtbvĚśÝđŘžľCÉŹf_ÍĺŤČOiđ°Üľ˝D
uŔĹÍCąĚć¤ČÉŹf_ĚĹßĚWđCíŠčâˇĐîľÜˇD
200:PRQlÚĚfłń
22/02/03 07:10:16.37 azzG9pAA.net
uąęǢËvuąęǢËvžÁÄ\ÁÄéŻÇ
ťęĚ˝ŞďĚIÉǤǢńžćEÜÝH˘ěY
201:PRQlÚĚfłń
22/02/04 16:10:27.26 2uUUa+ra.net
žÁ˝ŠŞĹČńŠ˘ÄÝëć
ŻČ˘ČçA10NROMę
202:PRQlÚĚfłń
22/02/06 12:08:54.90 dcjQr8w9.net
ąęŞŠčŐ˘Ë
URLŘݸ(tsujimotter.)ÍÄČuO/entry/affine-scheme-2
tsujimotterĚm[gubN
2019-05-07
AtBXL[ĆÍ˝žë¤Š(2)
OńÍAtBXL[Ěč`ÉüŻÄAÂĚXyNgĆUXL[ĘƢ¤TOđĐîľÜľ˝BĘŞüÁ˝ĚĹAÂĚXyNgŞĘóÔÉČčÜľ˝B
ĄúÍAĘóÔĚăĚ \˘w Şe[}šBĹIIÉÍAAtBXL[đč`ˇéĆąëÜŢŤ˝˘Ćv˘ÜˇB
{LĚÚF
4. \˘w
ă˝lĚĚAiW[
\˘wĚč`
ďĚáFX = Spec(Z) Ěę
OwĆw
pęĚč`
5. AtBXL[Ěč`
AtBXL[ĚďĚá1FSpec(Z)Ěę
AtBXL[ĚďĚá2FSpec(O_K)ĚęiăĚĚŽÂj
AtBXL[ĚďĚá3FSpec(K)ĚęiĚĚęj
¨íčÉ
QlśŁ
ńÍążç
203:PRQlÚĚfłń
22/02/06 13:08:03.55 dcjQr8w9.net
ąęŞŠčŐ˘Ë
URLŘݸ(tsujimotter)ÍÄČuO/entry/affine-scheme-1
tsujimotterĚm[gubN
2019-05-06
AtBXL[ĆÍ˝žë¤Š(1)
ćPi{LjF
1. ăô˝Ěî{
2. ÂĚXyNg
3. UXL[Ę
ćQi5/7öJ\čjF
4. \˘w
5. AtBXL[Ěč`
ćRi5/8öJ\čjF
6. AtBXL[ĚË
7. AtBXL[ĚËĚďĚá
8. ÜĆß
204:PRQlÚĚfłń
22/02/10 11:24:21.71 GluAcDmn.net
A[xô˝wĚiW ŻTęY w'74Ş12022N1
ćčAIUTÖALq˛
P15
6@ASYIA[xô˝wĆPA[xô˝w
2ßĹĚî{e\zCĚŕeÍCA[xă˝lĚÍťĚî{ŽSnńŠçełfłęéC Ƣ
¤ŕĚĹ Á˝DťľÄC ťĚ莝Šé2ßĚÎA[xŤâ3ßĚâÎA[xŤÍC
ÇżçŕCńÂĚ(A[xIĹ ë¤jă˝lĚ'X'Ć'Y'ŞpÓłę˝ŰĚCťęçĚÔĚ
Ż^ËĆC ťęçĚî{QĚÔĚAąŻ^ËĆĚÖWđâčƾĢéD
ÂÜčC ąĚ莝ÉćéeA[xŤ'̤ĆÍCĺGcÉžŚÎC
KŘČă˝lĚĚȡɧŔłę˝'Î1'Ƣ¤ÖčĚ[ŤâŔŤĆ˘Á˝ŤżĚ¤Ĺ éĆvńłęéD
ťľÄC ąĚęCc_ɾξÎoęˇéeQ_ICƢ¤pęÍC
eî{QĚÔĚCÓĚAąŻ^ËĹŰ˝ęéCƢ¤ŤżđÓĄˇéD
]ÍCî{e\z'ɨŻéeł'ĆÍ˝ŠC Ƣ¤âđüßÄŠÂßźľ, [60], {61], [63]É
¨˘ÄC eASYIČĎ_ÉćéA[xô˝w'C
ťľÄC ćčˇ`ČggÝĆľÄĚPA[xô˝w(mono-anabelian geometry)Ƣ¤lŚđńĽľ˝D
ťĚă,ăqĚe[ŤĽŔŤĚĎ_ÉćéąęÜĹĚA[xô˝w'đoA[xô˝w(bi-anabelian geometry)ĆÄŃC
ąęçeńÂĚA[xô˝wCÉćĘđ^Ś˝D
ASYIČĎ_ÉćéA[xô˝wĆÍCČPÉžÁľ܌ÎCČşĚć¤Čŕeđ
ÂA[xô˝w̤̹ĆĹ éD
ASYIA[xô˝w ^Śçę˝ă˝lĚXÉÎľÄCŰIČĘQÎ1(X)đ
eüÍf[^'ĆľÄC ťľÄCă˝lĚXÉtˇéô˝wIÎŰ(áŚÎXťęŠĚjđeoÍf[^'ơéeĘQ_IASY'đm§šćD
ťľÄCPA[xIA(mono-anabelian transport) (áŚÎ[65]đQĆ)Ƣ¤ggÝĹ
ĚťĚĘQ_IłASY̤ŞCPA[xô˝wĹ éDA[xô˝wĚĺ
ŤČpĹ éFŰ^Cq~
[_{66]-[69]ĹÍ, ąĚASYIA[xô˝wâ
PA[xô˝wŞSIČđđĘ˝ˇĚĹ éD
205:PRQlÚĚfłń
22/02/11 18:06:33.74 seCJnoFl.net
>>204
>A[xô˝wĚiW ŻTęY w'74Ş12022N1
>ćčAIUTÖALq˛
IUTÍA{ŰVçtž夊
ĄČçÎASĹĚłŔéĹľĺ¤
Ż A[xô˝wĚiWÍA
麏Ělqâ¨éĚzuA
{ŰâVçtĚlqĚLqÍ éŞ
¨éŗ́żüÁ˝LqÍȢ
ľŠľAOxĆŕxÍßçę
¨éĚlqŕTŞÍLłęĢé
ąęđÇńĹŠç
IUTđÇßÎ
IUTđđˇéĚÉ
ǢĆv¤
(Ql)
URLŘݸ(ja.wikipedia.org)
wSĹĚnx
3.5 łŔéŇi16Ş - 23Şj
y[WĹVX\ŚXbhĚőŢXębčĚj
[X¨ÜŠšXgĽIvVđ\ŚÉÂÔľ2ch
379úOÉXV/383 KB
S:undef