EVENT DETAILS AND ABSTRACT

Title: p-adic L-functions and Iwasawa theory --- an introduction, part II
Speaker: Professor Matthew Emerton
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

This is a continuation of last week's talk.

I will explain the construction of Kubota--Leopoldt p-adic L-function, which is a p-adic analytic function obtained by interpolating special values of the Riemann zeta function. I will then go on to explain the role that this p-adic L-function plays in describing the arithmetic of the cyclotomic extensions of the rational numbers. The key result in this direction is the so-called Main Conjecture of Iwasawa theory, which was proved by Mazur and Wiles in the 1980s. It represents the culmination of a long tradition of number theoretic investigation, reaching all the way back to the work of Kummer from the mid 1800s, who made the first general study of the arithmetic of cyclotomic fields.