Congruences between modular forms

被引：0
|
作者：
Thorne, Jack A. [1 ]
机构：
[1] Dept Pure Math & Math Stat, Wilberforce Rd, Cambridge, England
来源：
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2024年 / 134卷 / 01期
关键词：
Modular forms; Galois representations; Langlands programme; ADIC GALOIS REPRESENTATIONS; SERRES CONJECTURE; ELLIPTIC-CURVES; AUTOMORPHY; MULTIPLICITIES; FUNCTORIALITY; COHOMOLOGY; FONTAINE;
D O I：
10.1007/s12044-024-00776-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We survey the connections between modular forms and representations of Galois groups that are predicted by the Langlands programme. We focus in particular on the applications of congruences between modular forms (through automorphy lifting theorems) to an improved understanding of these connections, including the author's recent joint work with James Newton on the existence of the symmetric power liftings of Hilbert modular forms.
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页数：31
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