Sato-Tate groups of some weight 3 motives
Number Theory
2017-01-03 v4 Algebraic Geometry
Abstract
We establish the group-theoretic classification of Sato-Tate groups of self-dual motives of weight 3 with rational coefficients and Hodge numbers h^{3,0} = h^{2,1} = h^{1,2} = h^{0,3} = 1. We then describe families of motives that realize some of these Sato-Tate groups, and provide numerical evidence supporting equidistribution. One of these families arises in the middle cohomology of certain Calabi-Yau threefolds appearing in the Dwork quintic pencil; for motives in this family, our evidence suggests that the Sato-Tate group is always equal to the full unitary symplectic group USp(4).
Keywords
Cite
@article{arxiv.1212.0256,
title = {Sato-Tate groups of some weight 3 motives},
author = {Francesc Fité and Kiran S. Kedlaya and Andrew V. Sutherland},
journal= {arXiv preprint arXiv:1212.0256},
year = {2017}
}
Comments
Minor edits to correct typos and address LMFDB modular form label changes