Arithmetic of low-dimensional abelian varieties
(June 3-7, 2019)
This workshop is an activity of the Simons Collaboration 'Arithmetic Geometry, Number Theory, and Computation' and is supported by the Simons Foundation.
In this workshop, we will explore a number of themes in the arithmetic of abelian varieties of low dimension (typically dimension 2--4), with a focus on computational aspects. Topics will include the study of torsion points, Galois representations, endomorphism rings, Sato-Tate distributions, Mumford-Tate groups, complex and p-adic analytic aspects, L-functions, rational points, and so on. We also seek to classify and tabulate these objects, in particular to understand explicitly the underlying moduli spaces (with specified polarization, endomorphism, and torsion structure), and to find examples of abelian varieties exhibiting special behavior. Finally, we will pursue connections with related areas, including the theory of modular forms, related algebraic varieties (e.g., K3 surfaces), and special values of L-functions.
Our goal is for the workshop to bring together researchers working on abelian varieties in a number of facets to establish collaborations, develop algorithms, and stimulate further research.