FINITENESS THEOREMS FOR POTENTIALLY EQUIVALENT GALOIS REPRESENTATIONS: EXTENSION OF FALTINGS' FINITENESS CRITERIA

被引：1

作者：

Das, Plawan ^{[1
]}

Rajan, C. S. ^{[2
]}

机构：

[1] Chennai Math Inst, H1 Sipcot IT Pk, Kelambakkam 603103, India

[2] Tata Inst Fundamental Res, Homi Bhabha Rd, Mumbai 400005, India

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 08期

关键词：

D O I：

10.1090/proc/15856

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the relationship between potential equivalence and character theory; we observe that potential equivalence of a representation rho is determined by an equality of an m-power character g -> Tr(rho(g(m))) for some natural number m. Using this, we extend Faltings' finiteness criteria to determine the equivalence of two P-adic, semisimple representations of the absolute Galois group of a number field, to the context of potential equivalence. We also discuss finiteness results for twist unramified representations.

引用

页码：3189 / 3200

页数：12

共 13 条

[11] SOME FINITENESS THEOREMS ON GALOIS CENTRALIZERS IN PRO-L MAPPING CLASS-GROUPS
NAKAMURA, H
TSUNOGAI, H
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1993, 441 : 115 - 144
[12] An upper bound and finiteness criteria for the Galois group of weighted walks with rational coefficients in the quarter plane
Jiang, Ruichao
Tavakoli, Javad
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COMPTES RENDUS MATHEMATIQUE, 2021, 359 (05) : 563 - 576
[13] Locally potentially equivalent two dimensional Galois representations and Frobenius fields of elliptic curves
Kulkarni, Manisha
Patankar, Vijay M.
Rajan, C. S.
JOURNAL OF NUMBER THEORY, 2016, 164 : 87 - 102

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