Homotopy theory of smooth compactifications of algebraic varieties
Algebraic Geometry
2013-09-03 v2 Algebraic Topology
Abstract
In this short note we show that the homotopy category of smooth compactifications of smooth algebraic varieties is equivalent to the homotopy category of smooth varieties over a field of characteristic zero. As an application we show that the functor sending a variety to the p-th step of the Hodge filtration of its complex cohomology is representable in the homotopy category of simplicial presheaves on smooth complex varieties. The main motivation are recent applications of homotopy theory to Deligne-Beilinson cohomology theories.
Keywords
Cite
@article{arxiv.1305.1777,
title = {Homotopy theory of smooth compactifications of algebraic varieties},
author = {Gereon Quick},
journal= {arXiv preprint arXiv:1305.1777},
year = {2013}
}
Comments
final version with minor changes