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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
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
Citation:
D. B. Kaledin, “Cyclotomic complexes”, Izv. Math., 77:5 (2013), 855–916
Linking options:
https://www.mathnet.ru/eng/im8008https://doi.org/10.1070/IM2013v077n05ABEH002663 https://www.mathnet.ru/eng/im/v77/i5/p3
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Abstract page: | 858 | Russian version PDF: | 209 | English version PDF: | 18 | References: | 55 | First page: | 16 |
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