Abstract
AbstractUsing 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.
Funder
Division of Mathematical Sciences
Publisher
Springer Science and Business Media LLC
Reference23 articles.
1. Bombieri, E., Vaaler, J.: On Siegel’s lemma. Invent. Math. 73(1), 11–32 (1983)
2. Chai, C.-L., Conrad, B., Oort, F.: Complex multiplication and lifting problems, Mathematical Surveys and Monographs, vol. 195. American Mathematical Society, Providence (2014)
3. Chi, W.C.: $$l$$-adic and $$\lambda $$-adic representations associated to abelian varieties defined over number fields. Am. J. Math. 114(2), 315–353 (1992)
4. Dixon, J.D.: Permutation representations and rational irreducibility. Bull. Aust. Math. Soc. 71(3), 493–503 (2005)
5. Dixon, J.D., Mortimer, B.: Permutation groups. Graduate Texts in Mathematics, vol. 163. Springer, New York (1996)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献