##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Christopher Davis

#### UC Irvine

## The Overconvergent de Rham-Witt complex

##### Abstract:

The aim of the talk is to describe the overconvergent de Rham-Witt complex. It is a subcomplex of the de Rham-Witt complex and it can be used to compute Monsky-Washnitzer cohomology for affine varieties, and rigid cohomology in general. (All our varieties are over a perfect field of characteristic p.) We will begin by reviewing Monsky-Washnitzer cohomology and the de Rham-Witt complex. Next we will define overconvergent Witt vectors and then the overconvergent de Rham-Witt complex. As time permits, we will say something about the proof of the comparison theorem between Monsky-Washnitzer cohomology and overconvergent de Rham-Witt ohomology. This is joint work with Andreas Langer and Thomas Zink.

Host: Kiran Kedlaya

### October 21, 2010

### 2:00 PM

### AP&M 7321

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