25/11/05 13:44:07.75 K/Lr81ky.net
>>257
>Not motivated by concern with logic, Kisin (2009b) extends and simplifies (Wiles, 1995), generally using geometry less than commutative algebra, visibly reducing the demands on set theory. And Kisin (2009a) completes a different proof of FLT by a strategy of Serre advanced by Khare and Wintenberger.
下記だね
References
Kisin, M. (2009a). Modularity of 2-adic Barsotti-Tate representations. Inventiones Mathematicae, 178(3):587–634.
Kisin, M. (2009b). Moduli of finite flat group schemes, and modularity. Annals of Mathematics, 170(3):1085–1180.
これを、検索すると(2009a)
URLﾘﾝｸ(www.researchgate.net)
Modularity of 2-adic Barsotti-Tate representations
December 2009Inventiones mathematicae 178(3):587-634
Abstract
We prove a modularity lifting theorem for two dimensional, 2-adic, potentially Barsotti-Tate representations. This proves hypothesis (H) of Khare-Wintenberger, and completes the proof of Serre’s conjecture. The main new ingredient is a classification of connected finite flat group schemes over rings of integers of finite extensions of ℚ2.
(2009b)：こちらはフルテキストが落とせるな
（This provides a more conceptual way of establishing the Shimura-Taniyama-Weil conjecture）
URLﾘﾝｸ(annals.math.princeton.edu)
Moduli of finite flat group schemes, and modularity By MARK KISIN
Abstract
We prove that, under some mild conditions, a two dimensional p-adic Galois representation which is residually modular and potentially Barsotti-Tate at p is modular.
This provides a more conceptual way of establishing the Shimura-Taniyama-Weil conjecture, especially for elliptic curves which acquire good reduction over a wildly ramified extension of 3.
The main ingredient is a new technique for analyzing flat deformation rings. It involves resolving them by spaces which parametrize finite f lat group scheme models of Galois representations.