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