刚性共轭自偶伽罗瓦表示的变形

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2024-05-31 DOI:10.1007/s10114-024-1409-x

Yi Feng Liu, Yi Chao Tian, Liang Xiao, Wei Zhang, Xin Wen Zhu

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引用次数: 0

摘要

本文研究共轭自偶伽罗瓦表示的变形。研究包括两个方面。首先，我们证明了一个共轭自偶伽罗瓦表示的 R=T 型定理，这个共轭自偶伽罗瓦表示的系数在有限域中，满足某个称为刚性的性质。其次，我们研究了附加于椭圆曲线对称幂的残差伽罗华表示族的刚性性质，以及正则代数共轭自偶尖顶表示的刚性性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Deformation of Rigid Conjugate Self-dual Galois Representations

In this article, we study deformations of conjugate self-dual Galois representations. The study is twofold. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field, satisfying a certain property called rigid. Second, we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve, as well as to a regular algebraic conjugate self-dual cuspidal representation.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.