##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Romyar Sharifi

#### University of Arizona

## Unramified Iwasawa modules

##### Abstract:

Iwasawa theory concerns the growth of arithmetic objects in towers of number fields. The unramified Iwasawa modules that are the inverse limits of p-parts of class groups up such a tower are central objects in the study of Iwasawa theory. I will discuss a variety of conjectures and results on the structure of unramified Iwasawa modules, along with applications. In particular, I intend to explain Iwasawa-theoretic refinements of Leopoldt's reflection principle which form part of joint work with Bleher, Chinburg, Greenberg, Kakde, Pappas, and Taylor.

Host: Cristian Popescu

### December 3, 2015

### 1:00 PM

### AP&M 7321

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