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Monodromy groups of Jacobians with definite quaternionic multiplication

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arxiv 2303.00804 v2 pith:6A4VLB4L submitted 2023-03-01 math.NT math.AG

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keywords fieldconnectedmonodromyabeliandefinitejacobiansmultiplicationquaternionic
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abstract

Let $A$ be an abelian variety over a number field. The connected monodromy field of $A$ is the minimal field over which the images of all the $\ell$-adic torsion representations have connected Zariski closure. We show that for all even $g \geq 4$, there exist infinitely many geometrically nonisogenous abelian varieties $A$ over $\mathbb{Q}$ of dimension $g$ where the connected monodromy field is strictly larger than the field of definition of the endomorphisms of $A$. Our construction arises from explicit families of hyperelliptic Jacobians with definite quaternionic multiplication.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Automorphism groups of curves with simple Jacobians

    math.AG 2026-07 conditional novelty 7.0 of 10

    Over an algebraically closed field of characteristic 0, the automorphism group of a curve with simple Jacobian must be cyclic of prime-power or two-prime order, a generalized quaternion group, or trivial, and every su...

  2. What makes an algebraic curve special?

    math.AG 2025-02 conditional novelty 3.0 of 10

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