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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年6月18日

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  • Keisuke Arai,
  • Yuuki Takai

摘要

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.