##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Peter Wear

#### UC San Diego

## Extended Robba rings and the Fargues-Fontaine curve

##### Abstract:

The Fargues-Fontaine curve is a fundamental object in p-adic Hodge theory. I will mention some of the important properties of the curve, then introduce the rings that are used to build the curve. These are the extended Robba rings; they share many properties with the one dimensional affinoid algebras of rigid analytic geometry. I will discuss these similarities, point out some key differences, and explain how to adapt some proofs from rigid geometry to bypass these differences. The pre-talk will give an overview of some of the basics of rigid analytic geometry.

Host: Claus Sorensen

### September 28, 2017

### 2:00 PM

### AP&M 7321

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