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arXiv · alg-geom/9507013

Descent, Motives and K-theory

Henri Gillet·Christophe Soule
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Abstract

To an arbitrary variety over a field of characteristic zero, we associate a complex of Chow motives, which is, up to homotopy, unique and bounded. We deduce that any variety has a natural Euler characteristic in the Grothendieck group of Chow motives. We show that the cohomology with integer coefficients of any singular variety over the complex numbers has a natural weight filtration. We define algebraic K-theory with "compact supports".

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Henri Gillet, Christophe Soule. 1995-07-21. Descent, Motives and K-theory. https://arxiv.org/abs/alg-geom/9507013

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