Topological Cyclic Homology of Schemes

By Thomas H. Geisser, L. Hesselholt. 2003

85 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3c623cb08022827f0ff29aa51ada7a40bb37c1da

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

K-theory and topological cyclic homology of henselian pairs (2018, methodology): “In addition, it relies heavily on the calculations of Geisser–Levine [28] and Geisser– Hesselholt [28] of p-adic algebraic K-theory and topological cyclic homology for smooth schemes in characteristic p.”
A universal characterization of higher algebraic K-theory (2010, background): “, see [21]) to regard TC as giving rise to a functor to pro-spectra — this variant of TC then does preserve filtered colimits.”
The Local Structure of Algebraic K-Theory (2012, methodology): “9 Topological cyclic homology of schemes and excision In [92], Geisser and Hesselholt extend the definition of topological cyclic homology to schemes by applying Thomason’s extension of the Godement construction.”
On the de Rham–Witt complex in mixed characteristic (2004, background): “Details may be found in [9], [8], [7], and [4].”
Localization theorems in topological Hochschild homology and topological cyclic homology (2008, methodology): “hinery of the construction of THHof small spectral categories that we develop in this paper; it is not known how to prove them using just a hypercohomology construction like that of GeisserHesselholt [16]. The paper is organizedas follows. In Section 2, we review the basic deﬁnitions for spectral ca”
Hermitian K-theory, derived equivalences and Karoubi's fundamental theorem (2012, background): “-th iterate of the S•-construction: S(n) i E = S|i ...S{z }i n E. This is a positive Ω-spectrum [Wal85, Proposition 1.5.3 and Remark thereafter]. It was given the structure of a symmetric spectrum in [GH99]. 4.2. The R•-construction. Recall [Sch10b, §2.3] that an exact category with weak equivalence”
Hyperdescent and étale K-theory (2019, methodology): “f this construction have been considered by Friedlander [Fri80, Fri82] and Dwyer-Friedlander [DF85] in the l-adic case (where l is invertible on the base) and in the p-adic case by Geisser-Hesselholt [GH99]. In this paper, we simply sheaﬁfy K-theory in the sense of [Lur09, Ch. 6]; this is slightly d”