New York Journal of Mathematics
Volume 19 (2013) 533-544


Gereon Quick

Homotopy theory of smooth compactifications of algebraic varieties

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Published: August 27, 2013
Keywords: Hodge filtration; motivic homotopy theory; smooth compactifications
Subject: 14F42; 14F35

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.

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Mathematisches Institut, WWU Münster, Einsteinstr. 62, 48149 Münster, Germany