Classes caractéristiques des schémas feuillets
Classes caractéristiques des schémas feuilletés
摘要：
本文研究了格式上的派生叶理的概念和任意特征的派生格式。我们介绍了霍奇过滤相关的派生叶理，functorialy过滤器派生德拉姆上同调。我们使用这种过滤研究消失的结果陈类的完美的复杂赋予沿派生叶理的连接。作为应用，我们证明了一个积极的特征版本的Bott的消灭定理和更一般的存在残留的叶状奇异由于Baum-Bott在特征零。
英文摘要：
We study a notion of derived foliations on schemes and derived schemes of arbitrary characteristics. We introduce the Hodge filtration associated to a derived foliation, which functorialy filters derived de Rham cohomology. We use this filtration to study vanishing results of Chern classes of perfect complexes endowed with connexions along derived foliations. As an application, we prove a positive characteristic version of Bott's vanishing theorem and more generally of existence of residues for foliations with singularities due to Baum-Bott in characteristic zero.
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