Sato-Tate groups of abelian threefolds

NUMBER THEORY

Speaker:

Francesc Fité - MIT

via Zoom Video Conferencing: https://harvard.zoom.us/j/136830668

The Sato-Tate group of an abelian variety A of dimension g defined over a number field is a compact real Lie subgroup of the unitary
simplectic group of degree 2g that conjecturally governs the limiting distribution of the normalized Frobenius elements acting on the Tate module
of A. In previous joint work with Kedlaya, Rotger and Sutherland, it was shown that there are 52 such subgroups (up to conjugacy) that occur as
Sato-Tate groups of abelian surfaces over number fields. In this talk I will present several aspects of the classification of the 410 subgroups (up
to conjugacy) of the unitary symplectic group of degree 6 that occur as the Sato-Tate groups of abelian threefolds over number fields. This is a joint
work with Kiran Kedlaya and Andrew Sutherland.