论文标题
二维Calabi-yau类别的整体猪头猜想
The integral Hodge conjecture for two-dimensional Calabi-Yau categories
论文作者
论文摘要
我们为类别制定了整体Hodge猜想的版本，证明了二维Calabi-yau类别的猜想，该类别适当地等效于K3或Abelian Surface的派生类别，并使用它来将其推定，以将其用于各种杂种的综合hodge猜想的案例。在此过程中，我们证明了对二维Calabi-yau类别家族的变异积分Hodge猜想的一种版本，以及此类家族中对象相对模量空间的一般平滑度结果。我们的机械还可以应用于中级雅各布人的结构，例如在派生类别中的标准，因为它们将其分为曲线的雅各布人之和。
We formulate a version of the integral Hodge conjecture for categories, prove the conjecture for two-dimensional Calabi-Yau categories which are suitably deformation equivalent to the derived category of a K3 or abelian surface, and use this to deduce cases of the usual integral Hodge conjecture for varieties. Along the way, we prove a version of the variational integral Hodge conjecture for families of two-dimensional Calabi-Yau categories, as well as a general smoothness result for relative moduli spaces of objects in such families. Our machinery also has applications to the structure of intermediate Jacobians, such as a criterion in terms of derived categories for when they split as a sum of Jacobians of curves.
