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Title: Angle ranks of abelian varieties
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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NSF-PAR ID:
10418453
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
Mathematische Annalen
Volume:
389
Issue:
1
ISSN:
0025-5831
Format(s):
Medium: X Size: p. 169-185
Size(s):
["p. 169-185"]
Sponsoring Org:
National Science Foundation
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