Endomorphism algebras of geometrically split genus 2 Jacobians over Q

Francesc Fité; Enric Florit; Xavier Guitart

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arXiv · 2212.11102

Endomorphism algebras of geometrically split genus 2 Jacobians over Q

Francesc Fité·Enric Florit·Xavier Guitart

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Abstract

The main result of [FG20] classifies the 92 geometric endomorphism algebras of geometrically split abelian surfaces defined over Q. We show that 54 of them arise as geometric endomorphism algebras of Jacobians of genus 2 curves defined over Q, and that the remaining 38 do not. In particular, we exhibit 38 examples of Qbar-isogeny classes of abelian surfaces defined over Q that do not contain any Jacobian of a genus 2 curve defined over Q, and for each of the 54 algebras that do arise we exhibit a curve realizing them.

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BibTeX RIS

Francesc Fité, Enric Florit, Xavier Guitart. 2022-12-21. Endomorphism algebras of geometrically split genus 2 Jacobians over Q. https://arxiv.org/abs/2212.11102

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