IUTを読むための用語集資料スレ2

IUTを読むための用語� ..

237:１３２人目の素数さん
22/04/29 06:37:49.57 b8gsErp4.net
＜q-parameter についてメモ＞
URLﾘﾝｸ(ivanfesenko.org)
ARITHMETIC DEFORMATION THEORY VIA
ARITHMETIC FUNDAMENTAL GROUPS AND NONARCHIMEDEAN THETA-FUNCTIONS,
NOTES ON THE WORK OF SHINICHI MOCHIZUKI
IVAN FESENKO
This text was published in Europ. J. Math. (2015) 1:405?440.
P9
If v is a bad reduction
valuation and Fv is the completion of F with respect to v, then the Tate curve F×
v /hqvi, where qv is the q-parameter of EF at v and hqvi is the cyclic group generated by qv, is isomorphic to EF(Fv), hqvi → the origin of
EF, see Ch.V of [44] and §5 Ch.II of [43].
P10
Define an idele qEF ∈ lim -→ A×k: its components at archimedean and good reduction valuations are taken to
be 1. Its components at places where EF has split multiplicative reduction are taken to be qv, where qv is the
q-parameter of the Tate elliptic curve EF(Fv) = F×v /hqvi.
The ultimate goal of the theory is to give a suitable bound from above on deg(qEF).
Fix a prime integer l > 3 which is relatively prime to the bad reduction valuations of EF, as well as to the
value nv of the local surjective discrete valuation of the q-parameter qv for each bad reduction valuation v.
P13
Let q ∈ L be a non-zero element of the maximal ideal of the ring of integers of L (this q will eventually be
taken to be the q-parameter qv of the Tate curve EF(Fv) ' F×v /hqvi, where L = Fv, for bad reduction primes v of
E, see Ch.5 of [44]).
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