title: Mixed motivic sheaves (and weights for them) exist if 'ordinary' mixed  motives do
metadata.name: dc.contributor.author
metadata.value: Mikhail V. Bondarko
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-04-07T11:59:15Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-04-07T11:59:15Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2015-01-02
metadata.lang: -
metadata.name: dc.identifier
metadata.value: 10.1112/S0010437X14007763
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Compositio Mathematica 151 (2015) 917-956
metadata.lang: -
metadata.name: dc.identifier.issn
metadata.value: 1570-5846
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/1901
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The goal of this paper is to prove: if certain 'standard' conjectures on
  motives over algebraically closed fields hold, then over any 'reasonable' $S$
  there exists a motivic $t$-structure for the category of Voevodsky's
  $S$-motives (as constructed by Cisinski and Deglise). If $S$ is 'very
  reasonable' (for example, of finite type over a field) then the heart of this
  $t$-structure (the category of mixed motivic sheaves over $S$) is endowed with
  a weight filtration with semi-simple factors. We also prove a certain 'motivic
  decomposition theorem' (assuming the conjectures mentioned) and characterize
  semi-simple motivic sheaves over $S$ in terms of those over its residue fields.
  Our main tool is the theory of weight structures. We actually prove somewhat
  more than the existence of a weight filtration for mixed motivic sheaves: we
  prove that the motivic $t$-structure is transversal to the Chow weight
  structure for $S$-motives (that was introduced previously and independently by
  D. Hebert and the author; weight structures and their transversality with
  t-structures were also defined by the author in recent papers). We also deduce
  several properties of mixed motivic sheaves from this fact. Our reasoning
  relies on the degeneration of Chow-weight spectral sequences for 'perverse
  'etale homology' (that we prove unconditionally); this statement also yields
  the existence of the Chow-weight filtration for such (co)homology that is
  strictly restricted by ('motivic') morphisms.
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 (Primary) 14F42 (Secondary), 19E15, 14F43, 18G40, 14C25,  14F20, 18E30, 13D15
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Mixed motivic sheaves (and weights for them) exist if 'ordinary' mixed  motives do
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
metadata.name: dcterms.publisher
metadata.value: Compositio Mathematica
metadata.lang: -
resources.filename: bcomp15.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/1901/1/bcomp15.pdf
resources.format: Adobe PDF
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