School of Mathematics and Statistics
Number Theory Seminar 

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 nontrivial automorphisms there are many possible curves C' over l which lift to C but are nonisomorphic 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. 