论文标题
Q
Endomorphism algebras of geometrically split genus 2 Jacobians over Q
论文作者
论文摘要
[FG20]的主要结果分类了在Q上定义的几何分裂的Abelian表面的92个几何内态代数。我们表明，其中54个是在Q属2曲线的Jacobians的几何内态代数中出现的，而其余的38则未定义。特别是，我们展示了在Q上定义的Abelian表面的QBAR衰减类别的38个示例，这些示例不包含Q属属2曲线的任何jacobian，而对于确实出现的54个代数中的每一个，我们都表现出一种实现它们的曲线。
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.
