Stephen Meagher

Friday 19 August, 4:05-4:55PM, Carslaw 375

Twisting Curves

Given a curve C over a field k, how do we "descend" this curve to a subfield l of k? For general curves, there is a unique answer. For curves with non-trivial automorphisms there are many possible curves C' over l which lift to C but are non-isomorphic as curves over l. The set of such curves are called forms or twists of C, and this set is in bijection with a certain Galois cohomology set. In this talk we show how this works and how to compute the forms for a particular family of genus 3 curves over a finite field.