12/07/22 08:34:57.65
>>73
> ４位数学の本 第47巻：これは一見まともに見えるが、いま紙の本だけって先端の数学から３周遅れの感あり。このスレに書いてきたように、wikipediaの英語版を巡って英語文献を見て、それを補うために紙の本を読むようにしないと・・
例えば、佐藤‐テイト予想
英語版
URLﾘﾝｸ(en.wikipedia.org)
Proofs and claims in progress
On March 18, 2006, Richard Taylor of Harvard University announced on his web page the final step of a proof,
joint with Laurent Clozel, Michael Harris, and Nicholas Shepherd-Barron, of the Sato?Tate conjecture for elliptic curves over totally real fields satisfying a certain condition: of having multiplicative reduction at some prime.[4]
Two of the three articles have since been published.[5]
Further results are conditional on improved forms of the Arthur?Selberg trace formula. Harris has a conditional proof of a result for the product of two elliptic curves (not isogenous) following from such a hypothetical trace formula.
As of 8 July 2008, Richard Taylor has posted on his website an article (joint work with Thomas Barnet-Lamb, David Geraghty, and Michael Harris)
which claims to prove a generalized version of the Sato?Tate conjecture for an arbitrary non-CM holomorphic modular form of weight greater than or equal to two,
by improving the potential modularity results of previous papers. They also assert that the prior issues involved with the trace formula have been solved by Michael Harris' "Book project"[8] and work of Sug Woo Shin.[9][10]
Generalisation
There are generalisations, involving the distribution of Frobenius elements in Galois groups involved in the Galois representations on etale cohomology. In particular there is a conjectural theory for curves of genus n > 1.
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More precise questions
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ここにダウンロードできる文献へのリンクがたくさんある。佐藤‐テイト予想を知りたいと思えば、まずこれを読んでその基礎として和書を見る・・