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Mumford-type Shimura curves contained in the Torelli locus
Published 30 Sep 2025 in math.AG and math.NT | (2510.00093v1)
Abstract: In this article we give explicit equations for two Shimura families of genus 4 curves whose Jacobians are abelian fourfolds of Mumford type. These are the first explicit examples of abelian varieties over $\mathbb{Q}$ with endomorphism algebra $\mathbb{Z}$ and additional Hodge tensors.
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