Tate module and bad reduction

Dokchitser, Tim; Dokchitser, Vladimir; Morgan, Adam

doi:10.1090/proc/15067

Tate module and bad reduction
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by Tim Dokchitser, Vladimir Dokchitser and Adam Morgan PDF

Proc. Amer. Math. Soc. 149 (2021), 1361-1372 Request permission

Abstract:

Let $C/K$ be a curve over a local field. We study the natural semilinear action of Galois on the minimal regular model of $C$ over a field $F$ where it becomes semistable. This allows us to describe the Galois action on the $l$-adic Tate module of the Jacobian of $C/K$ in terms of the special fibre of this model over $F$.

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