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Weights for Relative Motives: Relation with Mixed Complexes of Sheaves
- Source :
- International Mathematics Research Notices
- Publication Year :
- 2013
- Publisher :
- Oxford University Press (OUP), 2013.
-
Abstract
- The main goal of this paper is to define the so-called Chow weight structure for the category of Beilinson motives over any 'reasonable' base scheme $S$ (this is the version of Voevodsky's motives over $S$ defined by Cisinski and Deglise). We also study the functoriality properties of the Chow weight structure (they are very similar to the well-known functoriality of weights for mixed complexes of sheaves). As shown in a preceding paper, the Chow weight structure automatically yields an exact conservative weight complex functor (with values in $K^b(Chow(S))$). Here $Chow(S)$ is the heart of the Chow weight structure; it is 'generated' by motives of regular schemes that are projective over $S$. Besides, Grothendiek's group of $S$-motives is isomorphic to $K_0(Chow(S))$; we also define a certain 'motivic Euler characteristic' for $S$-schemes. We obtain (Chow)-weight spectral sequences and filtrations for any cohomology of motives; we discuss their relation to Beilinson's 'integral part' of motivic cohomology and to weights of mixed complexes of sheaves. For the study of the latter we introduce a new formalism of relative weight structures.<br />Comment: a few minor corrections made
- Subjects :
- General Mathematics
K-Theory and Homology (math.KT)
State (functional analysis)
14C15, 19E15, 14C25, 14F20, 14E18, 18E30, 13D15, 18G40
Mathematics - Algebraic Geometry
Mathematics::Algebraic Geometry
Work (electrical)
Mathematics::K-Theory and Homology
Mathematics::Category Theory
Mathematics - K-Theory and Homology
FOS: Mathematics
Relation (history of concept)
Algebraic Geometry (math.AG)
Mathematical economics
Mathematics
Subjects
Details
- ISSN :
- 16870247 and 10737928
- Volume :
- 2014
- Database :
- OpenAIRE
- Journal :
- International Mathematics Research Notices
- Accession number :
- edsair.doi.dedup.....bb6642fd8eacf5fc960cd6852aaaf2f9