Angle ranks of abelian varieties

2021/12/05 by Dupuy, Taylor, Kedlaya, Kiran S., Zureick-Brown, David
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.02455

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.

Related

• Galois groups of simple abelian varieties over finite fields and exceptional Tate classes
• Heights, ranks and regulators of abelian varieties
• Comparison of different Tate conjectures
• Counterexamples to a Conjecture of Ahmadi and Shparlinski
• Standard conjecture of Hodge type for powers of abelian varieties