The abelian part of a compatible system and l-independence of the Tate conjecture

Autor:	Hui, Chun Yin
Rok vydání:	2016
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	Let K be a number field and {V_l} be a rational strictly compatible system of semisimple Galois representations of K arising from geometry. Let G_l and V_l^ab be respectively the algebraic monodromy group and the maximal abelian subrepresentation of V_l for all l. We prove that the system {V_l^ab} is also a rational strictly compatible system under some group theoretic conditions, e.g., when G_l' is connected and satisfies Hypothesis A for some prime l'. As an application, we prove that the Tate conjecture for abelian variety X/K is independent of l if the algebraic monodromy groups of the Galois representations of X satisfy the required conditions. Comment: 22 pages. Accepted to Manuscripta Math
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1603.01283 Zobrazit plný text záznamu View this record from Arxiv