The Large Sieve and Galois Representations

Date
Authors
Zywina, David
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We describe a generalization of the large sieve to situations where the underlying groups are nonabelian, and give several applications to the arithmetic of abelian varieties. In our applications, we sieve the set of primes via the system of representations arising from the Galois action on the torsion points of an abelian variety. The resulting upper bounds require explicit character sum calculations, with stronger results holding if one assumes the Generalized Riemann Hypothesis.
Comment: 36 pages
Keywords
Mathematics - Number Theory, 11N35 (Primary) 11G05, 11F80 (Secondary)
Citation
Collections