RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 5, Pages 3–70 (Mi izv8008)  

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

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-33024
Ministry of Education and Science of the Russian Federation 11.G34.31.0023
Dynasty Foundation


DOI: https://doi.org/10.4213/im8008

Full text: PDF file (908 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2013, 77:5, 855–916

Bibliographic databases:

Document Type: Article
UDC: 512.736
MSC: 19D55, 14A22, 18G55
Received: 14.06.2012

Citation: D. B. Kaledin, “Cyclotomic complexes”, Izv. RAN. Ser. Mat., 77:5 (2013), 3–70; Izv. Math., 77:5 (2013), 855–916

Citation in format AMSBIB
\Bibitem{Kal13}
\by D.~B.~Kaledin
\paper Cyclotomic complexes
\jour Izv. RAN. Ser. Mat.
\yr 2013
\vol 77
\issue 5
\pages 3--70
\mathnet{http://mi.mathnet.ru/izv8008}
\crossref{https://doi.org/10.4213/im8008}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3137194}
\zmath{https://zbmath.org/?q=an:06236931}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013IzMat..77..855K}
\elib{http://elibrary.ru/item.asp?id=20359201}
\transl
\jour Izv. Math.
\yr 2013
\vol 77
\issue 5
\pages 855--916
\crossref{https://doi.org/10.1070/IM2013v077n05ABEH002663}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000326377700001}
\elib{http://elibrary.ru/item.asp?id=21890885}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84888083947}


Linking options:
  • http://mi.mathnet.ru/eng/izv8008
  • https://doi.org/10.4213/im8008
  • http://mi.mathnet.ru/eng/izv/v77/i5/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:553
    Full text:35
    References:19
    First page:16

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018