0181現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE
2019/11/26(火) 23:13:42.54ID:oYs7jyeH>楕円曲線のホッジ・アラケロフ理論は、アラケロフ理論(英語版)(Arakelov theory)のフレームワークで考える p-進ホッジ理論(英語版)(p-adic Hodge thory)の楕円曲線についての類似理論である。
(参考)
https://en.wikipedia.org/wiki/P-adic_Hodge_theory
p-adic Hodge theory
(抜粋)
The theory has its beginnings in Jean-Pierre Serre and John Tate's study of Tate modules of abelian varieties and the notion of Hodge?Tate representation.
Hodge?Tate representations are related to certain decompositions of p-adic cohomology theories analogous to the Hodge decomposition, hence the name p-adic Hodge theory.
Further developments were inspired by properties of p-adic Galois representations arising from the etale cohomology of varieties. Jean-Marc Fontaine introduced many of the basic concepts of the field.