Cofibrant models of diagrams: mixed Hodge structures in rational homotopy
Cofibrant models of diagrams: mixed Hodge structures in rational homotopy
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图的协斐伦模型：有理同伦中的混合 Hodge 结构
DOI：
10.1090/s0002-9947-2014-06405-2
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
J. Cirici
中科院分区：
文献类型：
--
作者：
J. Cirici
我们研究了某种类型的图类别的同伦理论，这些图类别的顶点位于具有函子路径的变量类别中，从而可以根据共纤维对象很好地计算同伦类别。该理论应用于微分分级代数的混合Hodge图范畴。使用沙利文的最小模型，我们证明了混合霍奇复形上贝林森定理的乘法版本。因此，我们获得了复代数簇有理同伦型上的混合 Hodge 结构的函子性。在这种情况下，摩根理论获得的同伦群上的混合霍奇结构遵循混合霍奇图不可分解的导出函子。
We study the homotopy theory of a certain type of diagram categories whose vertices are in variable categories with a functorial path, leading to a good calculation of the homotopy category in terms of cofibrant objects. The theory is applied to the category of mixed Hodge diagrams of differential graded algebras. Using Sullivan's minimal models, we prove a multiplicative version of Beilinson's Theorem on mixed Hodge complexes. As a consequence, we obtain functoriality for the mixed Hodge structures on the rational homotopy type of complex algebraic varieties. In this context, the mixed Hodge structures on homotopy groups obtained by Morgan's theory follow from the derived functor of the indecomposables of mixed Hodge diagrams.