Potential automorphy of certain non self-dual 3-dimensional Galois representations

Konstantin Miagkov

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arXiv · 2405.02970

Potential automorphy of certain non self-dual 3-dimensional Galois representations

Konstantin Miagkov

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Abstract

In a series of papers, van Geemen and Top have defined a family of surfaces $S_z$ indexed by a nonzero integer parameter $z$, and a compatible family of 3-dimensional Galois representations over $\Q(i)$ attached to each surface. In this note we use recent advancements in potential automorphy and automorphy lifting to show that these compatible families are potentially automophic for all values of $z$, and hence that their L-functions have analytic continuation and a functional equation.

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Konstantin Miagkov. 2024-05-05. Potential automorphy of certain non self-dual 3-dimensional Galois representations. https://arxiv.org/abs/2405.02970

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