English

Abelian varieties, quaternion trick and endomorphisms

Algebraic Geometry 2022-02-01 v5 Number Theory

Abstract

Let XX be a polarized abelian variety over a field KK. Let OO be a ring with an involution that acts on XX and this action is compatible with the polarization. We prove that the natural action of OO on (X×Xt)4(X \times X^t)^4 is compatible with a certain principal polarization.

Keywords

Cite

@article{arxiv.2010.07995,
  title  = {Abelian varieties, quaternion trick and endomorphisms},
  author = {Yuri G. Zarhin},
  journal= {arXiv preprint arXiv:2010.07995},
  year   = {2022}
}

Comments

6 pages

R2 v1 2026-06-23T19:23:14.239Z