Sato-Tale groups and automorphy for nongeneric genus 2 curves

Andrew Booker
Thu, May 10, 2018
PIMS, University of Calgary
PIMS CRG in Explicit Methods for Abelian Varieties
I will describe recent joint work with Jeroen Sijsling, Drew Sutherland, John Voight and Dan Yasaki on genus 2 curves over Q. Our work has three primary goals: (1) produce an extensive table of genus 2 curves and their associated invariants; (2) explain the various Sato-Tate groups that arise in terms of functoriality; (3) prove at least one example of modularity for each nongeneric Sato-Tate group. Goal (1) was achieved in arXiv:1602.03715, with the data accessible inthe LMFDB, while goals (2) and (3) are in progress.