Angle ranks of abelian varieties

Abstract Using the formalism of Newton hyperplane arrangements, we resolve open questions regarding angle rank left over from work first two authors with Roe and Vincent. As a consequence end up generalizing theorems Lenstra–Zarhin Tankeev proving several new cases Tate conjecture for abelian varieties finite fields. We also obtain an effective version recent theorem Zarhin bounding heights coefficients in multiplicative relations among Frobenius eigenvalues.