Descent, Motives and K-theory

1995/07/21 by Henri Gillet, Gillet, Henri, Christophe Soulé +1 · 4 citations
Computer Science · #Algebraic Geometry (math.AG) #FOS: Mathematics #Face and Expression Recognition

paper · pdf · doi:10.48550/arxiv.alg-geom/9507013

openalex publication_date 1995/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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".

Cited by

• Hodge Conjecture via Singular Varieties
• Wall-crossing formulas for framed objects
• Motivic classes of fixed-generators Hilbert schemes of unibranch curve singularities and Igusa zeta functions
• Extended operational Chow group and Lefschetz (1,1)-theorem

Related

• On Chow-pure cohomology and Euler characteristics for motives and\n varieties, and their relation to unramified cohomology and Brauer groups
• Motivic Weight Complexes for Arithmetic Varieties
• On Chow weight structures without projectivity and resolution of singularities
• Algebraic K-theory and cubical descent
• The chow weight structure for geometric motives of quotient stacks