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arXiv · 1908.08678

Drinfeld-Stuhler modules and the Hasse principle

Keisuke Arai·Satoshi Kondo·Mihran Papikian
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Abstract

We develop a theory of canonical isogeny characters of Drinfeld-Stuhler modules similar to the theory of canonical isogeny characters of abelian surfaces with quaternionic multiplication. We then apply this theory to give explicit criteria for the non-existence of rational points on Drinfeld-Stuhler modular varieties over the finite extensions of $\mathbb{F}_q(T)$. This allows us to produce explicit examples of Drinfeld-Stuhler curves violating the Hasse principle.

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Keisuke Arai, Satoshi Kondo, Mihran Papikian. 2019-08-23. Drinfeld-Stuhler modules and the Hasse principle. https://arxiv.org/abs/1908.08678

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