Date: Wednesday, January 07, 2015
Location: 4096 East Hall (4:00 PM to 6:00 PM)
Title: The Shafarevich conjecture for K3 surfaces
Abstract: 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. In 1983, Faltings proved this conjecture for curves and the analogous conjecture for polarized abelian surfaces. Building on the work of Faltings and Andre, we prove the stronger unpolarized Shafarevich conjecture for K3 surfaces. I'll begin with an introduction to K3 surfaces and their arithmetic, as well as the historical context for the Shafarevich conjecture, before explaining the proof of the theorem.
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Speaker: Yiwei She
Institution: University of Chicago
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