Local to global principles for homomorphisms of abelian schemes-Reference-Cited by-同舟云学术

Local to global principles for homomorphisms of abelian schemes

Published:2023-11 Issue:1 Volume:257 Page:281-312
ISSN:0021-2172
Container-title:Israel Journal of Mathematics
language:en
Short-container-title:Isr. J. Math.

Author:

Gajda Wojciech,Petersen Sebastian

Abstract

AbstractLet A and B be abelian varieties defined over the function field k(S) of a smooth algebraic variety S/k. We establish criteria, in terms of restriction maps to subvarieties of S, for existence of various important classes of k(S)-homomorphisms from A to B, e.g., for existence of k(S)-isogenies. Our main tools consist of Hilbertianity methods, Tate conjecture as proven by Tate, Zarhin and Faltings, and of the minuscule weights conjecture of Zarhin in the case when the base field is finite.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s11856-023-2542-4.pdf

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