Papers › Endomorphism algebras of geometrically split genus 2 Jacobians over Q
Endomorphism algebras of geometrically split genus 2 Jacobians over Q
Francesc Fité, Enric Florit, Xavier Guitart
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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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