An equivalent condition for abelian varieties over finite fields to have QM

Keisuke Arai; Yuuki Takai

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arXiv · 2311.11051

An equivalent condition for abelian varieties over finite fields to have QM

Keisuke Arai·Yuuki Takai

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Abstract

In this paper, we give an equivalent condition for an abelian variety over a finite field to have multiplication by a quaternion algebra over a number field. We prove the result by combining Tate's classification of the endomorphism algebras of abelian varieties over finite fields with Yu's criterion of the existence of homomorphisms between semi-simple algebras.

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Keisuke Arai, Yuuki Takai. 2023-11-18. An equivalent condition for abelian varieties over finite fields to have QM. https://arxiv.org/abs/2311.11051

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