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On some families of Jacobians with definite quaternionic multiplication

By John Voight

Appears in collection : SAGA - Symposium on Arithmetic Geometry and its Applications

Let $A$ be an abelian variety over a number field. The connected monodromy field of $A$ is the minimal field over which the image of the $l$-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. This is joint work with Victoria Cantoral-Farfan and Davide Lombardo.

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Citation data

  • DOI 10.24350/CIRM.V.20001303
  • Cite this video Voight, John (09/02/2023). On some families of Jacobians with definite quaternionic multiplication. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20001303
  • URL https://dx.doi.org/10.24350/CIRM.V.20001303

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