Cyclotomic complexes

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 sp...

Full description

Saved in:
Bibliographic Details
Published in:Izvestiya. Mathematics 2013-01, Vol.77 (5), p.855-916, Article 3
Main Author: Kaledin, D.
Format: Article
Language:English
Subjects:
Categories
Construction
cyclotomic complex
cyclotomic spectrum
filtered Dieudonné module
Homology
Mathematical analysis
Modules
Spectra
Topology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1064-5632
1607-0046
1468-4810
DOI:10.1070/IM2013v077n05ABEH002663