Recent developments in geometric Iwasawa theory

Joe Kramer-Miller, Lehigh University

Abstract: Iwasawa theory is a central topic in modern algebraic number theory. It studies the variation of arithmetic invariants along certain families of number fields (i.e. finite extensions of the rational numbers). Geometric Iwasawa theory aims to study invariants along families of curves (or higher dimensional objects) over finite fields. Most work on geometric Iwasawa theory has only considered arithmetic invariants. However, even the simplest examples show that arithmetic invariants only give a small picture of the rich geometric structures in play. Recently, there has been a great deal of work on geometric Iwasawa theory using finer geometric invariants. In this talk, I will give a brief overview of classical Iwasawa theory for number fields as well as the "arithmetic invariant" approach to geometric Iwasawa theory. Then I will describe recent work and conjectures on geometric invariants.

Tea and refreshments available at 3:00 p.m. in the Assmus Conference Room (CU 212).