##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Jonathan Sands

#### University of Vermont and UCSD

## Dedekind Zeta functions at s=-1 and the Fitting ideal of the tame kernel in a relative quadratic extension

##### Abstract:

Abstract: Brumer's conjecture states that Stickelberger elements combining values of L-functions at s=0 for an abelian extension of number fields E/F should annihilate the ideal class group of E when it is considered as module over the appropriate group ring. In some cases, an ideal obtained from these Stickelberger elements has been shown to equal a Fitting ideal connected with the ideal class group. We consider the analog of this at s=-1, in which the class group is replaced by the tame kernel, which we will define. For a field extension of degree 2, we show that there is an exact equality between the Fitting ideal of the tame kernel and the most natural higher Stickelberger ideal; the 2-part of this equality is conditional on the Birch-Tate conjecture.

Host: Cristian Popescu

### March 15, 2007

### 2:00 PM

### AP&M 7321

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