Deformation theory and zeta functions of curves over finite fields

Title:  Deformation theory and zeta functions of curves over finite fields

Speaker:  Stiofáin Fordham (UCD)

Date:  Monday, 29th February 2016

Time:  4pm

Location:  Agriculture. 1.01 (Seminar Room).


Abstract:

Abstract: In the 1960s, Bernard Dwork initiated the study of how the zeta function of a curve varies as one varies the curve inside of "a family". This has lead to an enormous amount of (very successful) further work since then by many others. In some cases the theory somehow allows one to deform the equation of a curve that one is interested in, to a "simpler curve" that one already knows something about. The relation of the zeta function of one to the other is then given by a p-adic differential equation. This talk will consist of a precise description of the previous and some of the work that has happened since, together with some emphasis on the case of Artin-Schreier curves over finite fields.


Series: Algebra