Irreducibility of geometric Galois representations and the Tate conjecture for a family of elliptic surfaces

Lian Duan; Xiyuan Wang

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arXiv · 2001.07818

Irreducibility of geometric Galois representations and the Tate conjecture for a family of elliptic surfaces

Lian Duan·Xiyuan Wang

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Abstract

Using Calegari's result on the Fontaine-Mazur conjecture, we study the irreducibility of pure, regular, rank 3 weakly compatible systems of self-dual l-adic representations. As a consequence, we prove that the Tate conjecture holds for a family of elliptic surfaces defined over Q with geometric genus bigger than 1.

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Lian Duan, Xiyuan Wang. 2020-01-21. Irreducibility of geometric Galois representations and the Tate conjecture for a family of elliptic surfaces. https://arxiv.org/abs/2001.07818

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