On the local constancy of certain mod p Galois representations

被引：1

作者：

Ganguli, Abhik ^{[1
]}

Kumar, Suneel ^{[1
]}

机构：

[1] Indian Inst Sci Educ & Res IISER Mohali, Dept Math Sci, Sect 81, Sas Nagar 140306, Punjab, India

来源：

RESEARCH IN NUMBER THEORY | 2024年 / 10卷 / 02期

关键词：

Reduction of crystalline representations; Mod p local Langlands; MODULAR-REPRESENTATIONS; CRYSTALLINE REPRESENTATIONS; REDUCTIONS; WEIGHT;

D O I：

10.1007/s40993-024-00538-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we study local constancy of the mod p reduction of certain 2-dimensional crystalline representations of Gal(Q(p)/Q(p)) using the mod p local Langlands correspondence. We prove local constancy in the weight space by giving an explicit lower bound on the local constancy radius centered around weights going up to (p-1)(2)+3 and the slope in (0, p-1) satisfying certain constraints. We establish the lower bound by determining explicitly the mod p reductions at nearby weights and applying a local constancy result of Berger.

引用

页数：43

共 26 条

[1]

Arsovski B, 2021, DOC MATH, V26, P1929

[2] IRREDUCIBLE MODULAR-REPRESENTATIONS OF GL2 OF A LOCAL-FIELD [J].