##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Cristian Popescu

#### UCSD

## Hecke characters and the Quillen K-theory of number fields

##### Abstract:

First, I will describe how our results (joint with Greither) on the Brumer-Stark conjecture lead to a new construction of Hecke characters for CM number fields, generalizing A. Weil's Jacobi sum Hecke characters. Second, I will show how the values of these characters can be used to construct special elements in the even K-groups of CM and totally real number fields. Several applications ensue: a general construction of Euler Systems in the odd K-theory of CM and totally real number fields; a K-theoretic reformulation (and potential proof strategy) of a classical and wide open conjecture of Iwasawa on class groups of cyclotomic fields; potential new insights into Hilbert's 12th problem for CM number fields etc. Time permitting, I will touch upon some of these applications as well. This is based on joint work with G. Banaszak (Poland).

### May 1, 2014

### 2:00 PM

### AP&M 7321

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