title: On Chow-weight homology of motivic complexes and its relation to motivic homology
metadata.name: dc.contributor.author
metadata.value: Bondarko, Mikhail V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kumallagov, David Z.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-12-18T16:31:36Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-12-18T16:31:36Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Bondarko M. V., Kumallagov D. Z. On Chow-weight homology of motivic complexes and its relation to motivic homology. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 4, pp. 560–587.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.401
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/21841
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper we study in detail the so-called Chow-weight homology of Voevodsky motivic
  complexes and relate it to motivic homology. We generalize earlier results and prove that
  the vanishing of higher motivic homology groups of a motif M implies similar vanishing
  for its Chow-weight homology along with effectivity properties of the higher terms of its
  weight complex t(M) and of higher Deligne weight quotients of its cohomology. Applying
  this statement to motives with compact support we obtain a similar relation between the
  vanishing of Chow groups and the cohomology with compact support of varieties. Moreover,
  we prove that if higher motivic homology groups of a geometric motif or a variety over a
  universal domain are torsion (in a certain “range”) then the exponents of these groups are
  uniformly bounded. To prove our main results we study Voevodsky slices of motives. Since
  the slice functors do not respect the compactness of motives, the results of the previous Chow-weight homology paper are not sufficient for our purposes; this is our main reason
  to extend them to (wChow-bounded below) motivic complexes.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: motives
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: triangulated categories
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Chow groups
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: weight structures
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Chow-weight homology
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Deligne filtration
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: effectivity
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On Chow-weight homology of motivic complexes and its relation to motivic homology
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 560-587.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/21841/1/560-587.pdf
resources.format: Adobe PDF
resources.size: 469,57 kB