Cyclotomic complexes

Details Cyclotomic complexes Cyclotomic complexes

2010-03-14

arxiv.org/abs/1003.2810v1

Mathematics

Algebraic Topology

77 pages, LaTeX2e. Preliminary version -- comments welcome!

Scientific paper

We construct a triangulated category of cyclotomic complexes, a homological counterpart of cyclotomic spectra of Bokstedt and Madsen. We also construct a version of the Topological Cyclic Homology functor TC for cyclotomic complexes, and an equivariant homology functor from cycloctomic spectra to cyclotomic complexes which commutes with TC. Then on the other hand, we prove that the category of cyclotomic complexes is essentially a twisted 2-periodic derived category of the category of filtered Dieudonne modules of Fontaine and Lafaille. We also show that under some mild conditions, the functor TC on cyclotomic complexes is the syntomic cohomology functor.

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