title: One property of bounded complexes of discrete Fp[π]-modules
metadata.name: dc.contributor.author
metadata.value: Podkopaev, Oleg B.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-12-13T14:36:30Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-12-13T14:36:30Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Podkopaev O.B. One property of bounded complexes of discrete Fp[π]-modules. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 4, pp. 631–636.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.409
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15131
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The goal of this note is to give a proof of the following proposition. Let π be a profinite group
  and K
  ∗ be a bounded complex of discrete Fp[π]-modules. Assume all Hi(K
  ∗
  ) are finite
  abelian groups. Then there exists a quasiisomorphism L
  ∗ −→ K
  ∗, where L
  ∗ is a bounded
  complex of discrete Fp[π]-modules such that all Li are finite abelian groups. This is an
  analogue for discrete Fp[π]-modules of a well-known lemma about bounded complexes of Amodules
  (say, concentrated in nonnegative degrees), where A is a Noetherian commutative
  ring, that establishes the existence of a quasiisomorphism between any such complex and
  a complex of finitely generated A-modules that are free except, possibly, the one in degree
  0. This lemma plays the key role in the proof of a base change theorem for cohomology of
  coherent sheaves on Noetherian schemes, that in turn, can be used to prove a theorem of
  Grothendieck about the behavior of dimensions of cohomology groups of a family of vector
  bundles on a flat family of varieties.
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 5 (63); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: profinite group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: discrete module
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: cohomology
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: One property of bounded complexes of discrete Fp[π]-modules
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 09-Podkopaev.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15131/1/09-Podkopaev.pdf
resources.format: Adobe PDF
resources.size: 274,84 kB