[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 55 (1002ﾚｽ)
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ﾘﾛｰﾄﾞ規制です｡10分ほどで解除するので､他のﾌﾞﾗｳｻﾞへ避難してください｡

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819(1): 2021/06/25(金)00:09 ID:EpKfSbds(3/6) AAS
>>818
つづき

外部ﾘﾝｸ:en.wikipedia.org
Shimura variety
Role in the Langlands program
Shimura varieties play an outstanding role in the Langlands program. The prototypical theorem, the Eichler?Shimura congruence relation, implies that the Hasse?Weil zeta function of a modular curve is a product of L-functions associated to explicitly determined modular forms of weight 2.
Indeed, it was in the process of generalization of this theorem that Goro Shimura introduced his varieties and proved his reciprocity law.
Zeta functions of Shimura varieties associated with the group GL2 over other number fields and its inner forms (i.e. multiplicative groups of quaternion algebras) were studied by Eichler, Shimura, Kuga, Sato, and Ihara.
On the basis of their results, Robert Langlands made a prediction that the Hasse-Weil zeta function of any algebraic variety W defined over a number field would be a product of positive and negative powers of automorphic L-functions, i.e. it should arise from a collection of automorphic representations.[1] However philosophically natural it may be to expect such a description, statements of this type have only been proved when W is a Shimura variety.[4]
In the words of Langlands:
省3

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820(2): 2021/06/25(金)05:54 ID:WmyQCodS(1/11) AAS
>>817-819
足立恒雄の志村五郎についてのツイート。

「学者として偉いということと
　人格的に問題があるということとは
　まったく独立である」

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