Algebraic Geometry Seminar

The Shafarevich Conjecture for K3 Surfaces

Speaker: Yiwei Shi, Columbia University

Location: Warren Weaver Hall 201

Date: Tuesday, March 8, 2016, 3:30 p.m.


Let K be a number field, S a finite set of places of K, and g a positive integer. Shafarevich made the following conjecture for higher genus curves: the set of isomorphism classes of genus g curves defined over K and with good reduction outside of S is finite. Faltings proved this conjecture for curves and the analogous conjecture for polarized abelian surfaces and Zarhin removed the necessity of specifying a polarization. Building on the work of Faltings and Andre, we prove the unpolarized Shafarevich conjecture for K3 surfaces.