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Angle ranks of abelian varieties

https://doi.org/10.1007/s00208-023-02633-7

Dupuy, Taylor; Kedlaya, Kiran S.; Zureick-Brown, David (June 2023, Mathematische Annalen)

Abstract Using the formalism of Newton hyperplane arrangements, we resolve the open questions regarding angle rank left over from work of the first two authors with Roe and Vincent. 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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Counterexamples to a Conjecture of Ahmadi and Shparlinski

https://doi.org/10.1080/10586458.2021.1980463

Dupuy, Taylor; Kedlaya, Kiran; Roe, David; Vincent, Christelle (January 2021, Experimental Mathematics)

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Isogeny classes of abelian varieties over finite fields in the LMFDB

https://doi.org/10.1007/978-3-030-80914-0_13

Dupuy, Taylor; Kedlaya, Kiran S.; Roe, David; Vincent, Christelle (January 2021, Arithmetic Geometry, Number Theory, and Computation)

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Total p-differentials on schemes over Z/p2

https://doi.org/10.1016/j.jalgebra.2019.01.003

Dupuy, Taylor; Katz, Eric; Rabinoff, Joseph; Zureick-Brown, David (April 2019, Journal of Algebra)

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