Arithmetic of low-dimensional abelian varieties

ag.algebraic-geometry nt.number-theory
Start Date
2019-06-03 
End Date
2019-06-07 
Institution
ICERM 
City
Providence, RI 
Country
USA 
Meeting Type
conference 
Homepage
https://icerm.brown.edu/events/sc19-1-aldav/ 
Contact Name
Andrew V. Sutherland 

Description

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.

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