Spectral sequences associated to morphisms of locally free sheaves
Spectral sequences associated to morphisms of locally free sheaves
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与局部自由滑轮态射相关的谱序列
DOI：
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发表时间：
2014
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通讯作者：
S. Kovács
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作者：
S. Kovács
这是一个非常有用的工具，但要求F，F，F是局部自由的。本文的目的是给出一个在更一般的情况下产生类似谱序列的构造。更准确地说，目标是定义自然对象，如果态射F → F的上核不是局部自由的，则这些自然对象将扮演r−p F“的角色。这些对象将不再是单个层，而是OX -模的导出范畴的对象。然而，它们的函子和上同调性质将足够强大，使应用成为可能。这项工作起源于[Kovács 96]。其主要目标是使上同调论证在更一般的环境中起作用，而通向这一目标的途径是构造某些对象，这些对象的性质类似于光滑态射的相对德拉姆复形的组成部分。特别地，上述谱序列的类似物是在特殊情况下构造的（参见图1）。[同上]）。后来我改进了这个结构，后来我意识到类似的论点可以用在其他地方。所需的结构非常相似，但有些不同，参见。[Kov 97b，Kovács02]。似乎应该给一个
This is a very useful tool, but requires F,F,F be locally free. The aim of the present article is to give a construction that yields a similar spectral sequence in a more general case. More precisely, the goal is to define natural objects that will play the role of ∧r−p F ′′ if the cokernel of the morphism F → F is not locally free. These objects will not be single sheaves anymore, but objects of the derived category of OX -modules. Nevertheless their functorial and cohomological properties will be strong enough to make applications possible. This work originated in [Kovács96]. The principal goal was to make a cohomological argument work in a more general setting and the path to that goal led through the construction of certain objects whose properties resemble those of the components of the relative De Rham complex of a smooth morphism. In particular the analogue of the above spectral sequence was constructed in a special case (cf. [ibid.]). Subsequently I improved the construction and later I realized that similar arguments can be used elsewhere. The constructions needed were very similar, yet somewhat different cf. [Kovács97b, Kovács02]. It seems appropriate to give a