## Arithmetic Geometry and Number Theory RTG Seminar: Arithmetic finiteness results for Fano varieties and hypersurfaces

Seminar | March 19 | 3:10-5 p.m. | 748 Evans Hall

Ariyan Javanpeykar, Johannes Gutenberg University of Mainz

Department of Mathematics

Faltings proved that there are only finitely many abelian schemes of dimension $g$ over a fixed “arithmetic curve”. Similar finiteness results hold (for instance) for K3 surfaces (Andre + Y. She), smooth curves of fixed genus $g >1$ (Faltings), and cubic surfaces (Scholl). In this talk, we will investigate similar finiteness results for Fano varieties and hypersurfaces, and explain the “relation” with hyperbolic moduli spaces. For instance, we will explain how the Lang-Vojta conjecture implies vast generalizations of Faltings's finiteness result. This is joint work with Daniel Loughran.

Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.

yxy@berkeley.edu