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arXiv · 2511.07814

Superspecial primes for QM abelian surfaces over real number fields

Fangu Chen
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Abstract

Baba and Granath generalize Elkies' theorem on infinitude of supersingular primes for elliptic curves to abelian surfaces with quaternionic multiplication of discriminant $6$, whose field of moduli is $\mathbb{Q}$ and which is a Jacobian in characteristic $2$ and $3$. We extend the field of moduli to any number field with a real embedding, and weaken the local conditions at $2$ and $3$. The proof relies on the intersection theory of Heegner divisors on Shimura curves.

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Fangu Chen. 2025-11-11. Superspecial primes for QM abelian surfaces over real number fields. https://arxiv.org/abs/2511.07814

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