https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/244782 https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/244782/1/B76-01.pdf タイトル: Mono-anabelian Reconstruction of Number Fields (On the examination and further development of inter-universal Teichmuller theory) 著者: Hoshi, Yuichiro 発行日: Aug-2019 出版者: Research Institute for Mathematical Sciences, Kyoto University 誌名: 数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu
Abstract The Neukirch‐Uchida theorem asserts that every outer isomorphism between the absolute Galois groups of number fields arises from a uniquely determined isomorphism between the given number fields. In particular, the isomorphism class of a number field is completely deter‐ mined by the isomorphism class of the absolute Galois group of the number field. On the other hand, neither the Neukirch‐Uchida theorem nor the proof of this theorem yields an “explicit reconstruction of the given number field”. In other words, the Neukirch‐Uchida theorem only yields a bi‐anabelian reconstruction of the given number field. In the present paper, we discuss a mono‐anabelian reconstruction of the given number field. In particular, we give afunctorial “group‐theoretic” algorithm for reconstructing, from the absolute Galois group of a number field, the algebraic closure of the given number field [equipped with its natural Galois action] that gave rise to the given absolute Galois group.
