Contents Online
Mathematical Research Letters
Volume 28 (2021)
Number 5
Irreducibility of geometric Galois representations and the Tate conjecture for a family of elliptic surfaces
Pages: 1353 – 1378
DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n5.a4
Authors
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 $\ell$-adic representations. As a consequence, we prove that the Tate conjecture holds for a family of elliptic surfaces defined over $\mathbf{Q}$ with geometric genus bigger than $1$.
Received 27 April 2020
Accepted 25 August 2020
Published 16 August 2022