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Mathematics Colloquium

Tuesday, January 12, 2021
12:00pm to 1:00pm
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Thin sets of primes from reductions of abelian varieties and K3 surfaces
Yunqing Tang, Laboratoire de Mathématiques d'Orsay, CNRS & Université Paris-Sud,

For an elliptic curve E over the rational numbers, the work of Lang and Trotter provides heuristics for the behavior of the reductions of E modulo primes. The Lang-Trotter philosophy applies to abelian varieties, which are higher dimensional generalizations of elliptic curves, and predicts that some density zero sets of primes with certain reduction types ought to be infinite.

In this talk, I will discuss recent results that establish the infinitude of such sets for certain Kuga-Satake abelian varieties and K3 surfaces via intersection theory on their moduli spaces. Moreover, I will present an application of our results to the distribution of Hecke orbits in positive characteristic fields. These results are joint work with Ananth Shankar, with Ananth Shankar, Arul Shankar, and Salim Tayou, and with Davesh Maulik and Ananth Shankar.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.