##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Xin Tong

#### University of California, San Diego

## Towards a Hodge-Iwasawa Theory

##### Abstract:

With the motivation of generalizing the corresponding geometrization of Tamagawa-Iwasawa theory after Kedlaya-Pottharst, and with motivation of establishing the corresponding equivariant version of the relative p-adic Hodge theory after Kedlaya-Liu aiming at the deformation of representations of profinite fundamental groups and the family of \'etale local systems, we initiate the corresponding Hodge-Iwasawa theory with deep point of view and philosophy in mind from early work of Kato and Fukaya-Kato. In this talk, we are going to discuss some foundational results on the Hodge-Iwasawa modules and Hodge-Iwasawa sheaves, as well as some interesting investigation towards the goal in our mind, which are taken from our first paper in this series project.

### May 14, 2020

### 2:00 PM

### Zoom: https://kskedlaya.org/nts.cgi

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