Sato-Tate Groups of Abelian Threefolds

Francesc Fite, Universitat de Barcelona, Spain. Kiran S. Kedlaya, University of California San Diego, California. Andrew V. Sutherland, Massachusetts Institute of Technology, Cambridge, Massachusetts.

1. Introduction 2. Conventions 3. Background on Sato-Tate groups 4. The classification upper bound, part 1 5. The classification upper bound, part 2: The case $G^0 = \mathrm {U}(1)_3$ 6. Statistics on Sato-Tate distributions 7. Methods for explicit realizations of abelian threefolds 8. The lower bound via explicit realizations 9. Tables