Tate module and bad reduction

Tim Dokchitser, Vladimir Dokchitser, Adam Morgan

Published 2018-09-26Version 1

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.