Algebraic and topological aspects of the schematization functor
Algebraic and topological aspects of the schematization functor
复制标题
模式化函子的代数和拓扑方面
作者：
L. Katzarkov;T. Pantev;B. Toën
摘要 我们研究了图式同伦类型和图式化函子的一些基本性质。我们描述了图式同伦类型的两种不同的代数模型，即余简 Hopf 代数和等变余余代数，并为每个模型提供了图式化函子的显式构造。我们还研究了图式化函子的一些标准属性，这些属性有助于描述平滑射影复簇的图式化。在另一篇配套论文中，这些结果被用于在平滑射影簇的示意同伦型上构建非交换霍奇结构。
Abstract We study some basic properties of schematic homotopy types and the schematization functor. We describe two different algebraic models for schematic homotopy types, namely cosimplicial Hopf alegbras and equivariant cosimplicial algebras, and provide explicit constructions of the schematization functor for each of these models. We also investigate some standard properties of the schematization functor that are helpful for describing the schematization of smooth projective complex varieties. In a companion paper, these results are used in the construction of a non-abelian Hodge structure on the schematic homotopy type of a smooth projective variety.