##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Karen Acquista

#### Boston University

## The Weil group of a 2-local field

##### Abstract:

I will explain the cohomological approach to local class field theory, and how it generalizes to higher local fields. For example, a 2-local field $K$ is a complete discrete valuation field with residue field a local field; class field theory for K states, in part, that there is an Artin map from $K_2(K)$ to the abelianized absolute Galois group of $K$. I will show how the cohomological approach can be used to construct a Weil group for any finite extension of 2-local fields.

Host: Cristian Popescu

### October 25, 2007

### 2:00 PM

### AP&M 7321

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