Injective resolutions of BG and derived moduli spaces of local systems
Injective resolutions of BG and derived moduli spaces of local systems
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BG 的内射分辨率和局部系统的导出模空间
DOI：
10.1016/s0022-4049(99)00109-7
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发表时间：
1997
影响因子：
0.8
通讯作者：
M. Kapranov
中科院分区：
文献类型：
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作者：
M. Kapranov
Deligne、Drinfeld和Kontsevich曾多次建议，变形理论的经典问题中出现的所有模空间都应该扩展到自然的“导出”模空间，这些模空间在适当的意义上总是光滑的，并且其切空间涉及无穷小自同构层的整个上同调，而不仅仅是H1。在本说明中，我们给出了一个代数结构的最简单的一类模空间，即模的局部系统（表示的基本群）的这种扩展。
It was suggested on several occasions by Deligne, Drinfeld and Kontsevich that all the moduli spaces arising in the classical problems of deformation theory should be extended to natural “derived” moduli spaces which are always smooth in an appropriate sense and whose tangent spaces involve the entire cohomology of the sheaf of infinitesimal automorphisms, not just H1. In this note we give an algebraic construction of such an extension for the simplest class of moduli spaces, namely for moduli of local systems (representations of the fundamental group).