title: Weights for relative motives; relation with mixed complexes of sheaves
metadata.name: dc.contributor.author
metadata.value: Mikhail V. Bondarko
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-04-07T12:31:53Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-04-07T12:31:53Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2014
metadata.lang: -
metadata.name: dc.identifier
metadata.value: 10.1093/imrn/rnt088
metadata.lang: -
metadata.name: dc.identifier.issn
metadata.value: 10.1093/imrn/rnt088
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/1903
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by RFBR (grants no. 11-01-00588 and 12-01-33057) and by the Saint-Petersburg State University research grant no. 6.38.75.2011
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Mathematics - Algebraic Geometry
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Mathematics - Algebraic Geometry
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Mathematics - K-Theory and Homology
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: 14C15, 19E15, 14C25, 14F20, 14E18, 18E30, 13D15, 18G40
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Weights for relative motives; relation with mixed complexes of sheaves
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: brelmotdim (1).pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/1903/4/brelmotdim%20%281%29.pdf
resources.format: Adobe PDF
resources.size: 644,13 kB