Topological cyclic homology

General Introduction
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Search results
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Online References
Hesselholt and Geisser: Topological cyclic homology of schemes
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Paper References
Bokstedt, Hsiang, Madsen: The cyclotomic trace and algebraic Ktheory of spaces. (1993)
Geisser in Ktheory handbook (includes applications to arithmetic geometry and relations to etale Ktheory). See memo notes!
Hesselholt in Ktheory handbook.
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
On the descent proplem for topological cyclic homology and algebraic Ktheory, by Stavros Tsalidis: K0329
Geisser and Hesselholt: Ktheory and topological cyclic homology of smooth schemes over discrete valuation rings
McCarthy: Relative algebraic Ktheory and topological cyclic homology (1997)
Preprint in progress of Rognes: Homotopy operations in TC(*; p)
Preprint in progress of Rognes: Algebraic models for topological cyclic homology and Whitehead spectra of simply connected spaces
Preprint in progress of Rognes: Algebraic Ktheory of group rings and topological cyclic homology
arXiv:1003.2810 Cyclotomic complexes from arXiv Front: math.AT by D. Kaledin 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 2periodic 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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Other Information
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