##### Department of Mathematics,

University of California San Diego

****************************

### Math 208 - Algebraic Geometry

## Daniel Litt

#### UGA

## The section conjecture at the boundary of moduli space

##### Abstract:

Grothendieck's section conjecture predicts that over arithmetically interesting fields (e.g. number fields or p-adic fields), rational points on a smooth projective curve X of genus at least 2 can be detected via the arithmetic of the etale fundamental group of X. We construct infinitely many curves of each genus satisfying the section conjecture in interesting ways, building on work of Stix, Harari, and Szamuely. The main input to our result is an analysis of the degeneration of certain torsion cohomology classes on the moduli space of curves at various boundary components. This is (preliminary) joint work with Padmavathi Srinivasan, Wanlin Li, and Nick Salter.

Host: James McKernan

### April 3, 2020

### 2:00 PM

****************************