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arXiv · 2112.02455

Angle ranks of abelian varieties

Taylor Dupuy·Kiran S. Kedlaya·David Zureick-Brown
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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.

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Taylor Dupuy, Kiran S. Kedlaya, David Zureick-Brown. 2021-12-05. Angle ranks of abelian varieties. https://arxiv.org/abs/2112.02455

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