Local Galois representations for higher genus curves

Lead Research Organisation: University of Bristol
Department Name: Mathematics

Abstract

For a curve defined over a p-adic field, one of its most important invariants is the attached Galois representation, the action of the absolute Galois group on the torsion points of the Jacobian. The problem is to understand which Galois groups, and in particular which inertia groups, can occur in these representations for curves of a given genus. For elliptic curves this theory is classical, and the classification is well-known. In higher genus the situation is not as well understood, but recent developments in the theory of curves, their models and Jacobians should help to study this question.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509619/1 01/10/2016 30/09/2021
1961436 Studentship EP/N509619/1 18/09/2017 31/03/2021 Nirvana Coppola