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. Introduction2. Conventions3. Background on Sato-Tate groups4. The classification upper bound, part 15. The classification upper bound, part 2: The case $G^0 = \mathrm {U}(1)_3$6. Statistics on Sato-Tate distributions7. Methods for explicit realizations of abelian threefolds8. The lower bound via explicit realizations9. Tables

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. Introduction2. Conventions3. Background on Sato-Tate groups4. The classification upper bound, part 15. The classification upper bound, part 2: The case $G^0 = \mathrm {U}(1)_3$6. Statistics on Sato-Tate distributions7. Methods for explicit realizations of abelian threefolds8. The lower bound via explicit realizations9. Tables

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. Introduction2. Conventions3. Background on Sato-Tate groups4. The classification upper bound, part 15. The classification upper bound, part 2: The case $G^0 = \mathrm {U}(1)_3$6. Statistics on Sato-Tate distributions7. Methods for explicit realizations of abelian threefolds8. The lower bound via explicit realizations9. Tables