Grothendieck Duality for Deligne-Mumford Stacks
Grothendieck Duality for Deligne-Mumford Stacks
复制标题
Deligne-Mumford 栈的格洛腾迪克对偶性
DOI：
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发表时间：
2008
期刊：
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通讯作者：
Fabio Nironi
中科院分区：
文献类型：
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作者：
Fabio Nironi
证明了具有仿射对角线的代数堆的分离态射对偶函子的存在性；然后，我们明确地发展了紧态Deligne-Mumford堆栈的对偶性，特别关注了堆栈到其粗模空间的态射和可表征态射。我们显式地计算了代数闭域上光滑叠堆的对偶复合体，并证明了光滑紧Deligne-Mumford叠堆通常形式的Serre对偶性成立。我们还证明了一个适当的Cohen-Macaulay堆栈具有对偶层，当它是Gorenstein时它是可逆层。作为这一通用机制的一个应用，我们计算了驯服节点曲线的二值化轴。
We prove the existence of the dualizing functor for a separated morphism of algebraic stacks with affine diagonal; then we explicitly develop duality for compact Deligne-Mumford stacks focusing in particular on the morphism from a stack to its coarse moduli space and on representable morphisms. We explicitly compute the dualizing complex for a smooth stack over an algebraically closed field and prove that Serre duality holds for smooth compact Deligne-Mumford stacks in its usual form. We prove also that a proper Cohen-Macaulay stack has a dualizing sheaf and it is an invertible sheaf when it is Gorenstein. As an application of this general machinery we compute the dualizing sheaf of a tame nodal curve.