MIT Number Theory Seminar

Tuesday, September 15, 2020 at 4:30pm to 5:30pm

Virtual Event

Featured Speaker:  Brian Lawrence (University of Chicago)

Title:  The Shafarevich conjecture for hypersurfaces in abelian varieties

Abstract:  Let K be a number field, S a finite set of primes of O_K, and g a positive integer. Shafarevich conjectured, and Faltings proved, that there are only finitely many curves of genus g, defined over K and having good reduction outside S. Analogous results have been proven for other families, replacing "curves of genus g" with "K3 surfaces", "del Pezzo surfaces" etc.; these results are also called Shafarevich conjectures. There are good reasons to expect the Shafarevich conjecture to hold for many families of varieties: the moduli space should have only finitely many integral points.

Will Sawin and I prove this for hypersurfaces in abelian varieties of dimension not equal to 3.

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Bjorn Poonen, Number Theory Seminar, Number_Theory_Seminar, Andrew Sutherland


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