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arXiv · 1603.01283

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

Chun Yin Hui
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Abstract

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.

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Chun Yin Hui. 2016-03-03. The abelian part of a compatible system and l-independence of the Tate conjecture. https://arxiv.org/abs/1603.01283

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