Angle ranks of abelian varieties
Number Theory
2023-04-19 v3 Algebraic Geometry
Abstract
Using the formalism of Newton hyperplane arrangements, we resolve the open questions regarding angle rank left over from [DKRV20]. As a consequence we end up generalizing theorems of Lenstra--Zarhin and Tankeev proving several new cases of the Tate conjecture for abelian varieties over finite fields. We also obtain an effective version of a recent theorem of Zarhin bounding the heights of coefficients in multiplicative relations among Frobenius eigenvalues.
Cite
@article{arxiv.2112.02455,
title = {Angle ranks of abelian varieties},
author = {Taylor Dupuy and Kiran S. Kedlaya and David Zureick-Brown},
journal= {arXiv preprint arXiv:2112.02455},
year = {2023}
}
Comments
14 pages; v3: final refereed version; corrected bound and simplified proof of Theorem 1.8