关于微分与代数栈的 de Rham 上同调
代数几何
2007-05-23 v2 微分几何
摘要
我们引入栈上的余叶状结构概念。余叶状结构是一种可微结构的改变，相当于给出一个全可表光滑满态射。余叶状结构由其关联的李代数胚唯一确定。栈上的余叶状结构源于群胚上的平坦联络。群胚上的联络以自然方式推广了 gerbe 和丛上的联络。群胚上的平坦联络是态射空间的一个可积分布，与群胚结构相容，并且与源纤维和靶纤维都互补。栈的余叶状结构确定平坦群胚，直至 étale 等价。我们展示栈上的余叶状结构如何导出 Hodge 到 de Rham 谱序列的加细，其中 E1 项完全由向量丛值上同调群组成。我们的理论对可微栈、全纯栈和代数栈均适用。
引用
@article{arxiv.math/0410255,
title = {On the de Rham Cohomology of Differential and Algebraic Stacks},
author = {Kai Behrend},
journal= {arXiv preprint arXiv:math/0410255},
year = {2007}
}
备注
The paper has been completely rewritten. The technical core remains unchanged, but the context has changed entirely. We do not claim any more that additional structure on a stack is needed to obtain the Hodge to de Rham spectral sequence. We renamed "parallel structures" on groupoids "flat connections" and changed entirely the nature of the structure induced on stacks by flat groupoids. Citations and acknowledgements have been added. New version has 37 pages