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Izvestiya: Mathematics, 2013, Volume 77, Issue 5, Pages 855–916
DOI: https://doi.org/10.1070/IM2013v077n05ABEH002663
(Mi im8008)
 

This article is cited in 2 scientific papers (total in 2 papers)

Cyclotomic complexes

D. B. Kaledinab

a Steklov Mathematical Institute of the Russian Academy of Sciences
b Laboratory of algebraic geometry and its applications, Higher School of Economics, Moscow
References:
Abstract: We construct a triangulated category of cyclotomic complexes (homological analogues of the cyclotomic spectra of Bökstedt and Madsen) along with a version of the topological cyclic homology functor TC for cyclotomic complexes and an equivariant homology functor (commuting with TC) from cyclotomic spectra to cyclotomic complexes. We also prove that the category of cyclotomic complexes essentially coincides with the twisted 2-periodic derived category of the category of filtered Dieudonné modules, which were introduced by Fontaine and Lafaille. Under certain conditions we show that the functor TC on cyclotomic complexes is the syntomic cohomology functor.
Keywords: cyclotomic spectrum, cyclotomic complex, filtered Dieudonné module.
Received: 14.06.2012
Bibliographic databases:
Document Type: Article
UDC: 512.736
MSC: 19D55, 14A22, 18G55
Language: English
Original paper language: Russian
Citation: D. B. Kaledin, “Cyclotomic complexes”, Izv. Math., 77:5 (2013), 855–916
Citation in format AMSBIB
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\by D.~B.~Kaledin
\paper Cyclotomic complexes
\jour Izv. Math.
\yr 2013
\vol 77
\issue 5
\pages 855--916
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Linking options:
  • https://www.mathnet.ru/eng/im8008
  • https://doi.org/10.1070/IM2013v077n05ABEH002663
  • https://www.mathnet.ru/eng/im/v77/i5/p3
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:858
    Russian version PDF:209
    English version PDF:18
    References:55
    First page:16
     
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