Symmetric Spectra and Topological Hochschild Homology

By B. Shipley. 2000

79 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e63cbc511346a871eba11d0f18bec78c72522066

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Citations in the corpus

Uniqueness of the multiplicative cyclotomic trace (2011, background): “...∧ S1 UNIQUENESS OF THE MULTIPLICATIVE CYCLOTOMIC TRACE 31 deﬁnes a symmetric spectrum THH(C) = {THH(C;Sn)}. When C is a point-wise coﬁbrant spectral category, an elaboration of the work of Shipley [43] shows that there is a natural isomorphism in the stable category between this model of THH and ”
Spectra and symmetric spectra in general model categories (2000, background): “Nevertheless, in that case, every stable homotopy isomorphism is a stable equivalence [11, Theorem 3.1.11], and there is a replacement for the functor R1 constructed in [ 22 ].”
Model Categories of Diagram Spectra (2001, methodology): “We refer the reader to papers on particular categories [10, 11, 15, 21, 22, 24, 35, 39] and to [30] for discussions of the history, philosophy, advantages and disadvantages of the various approaches.”
Stable homotopy of algebraic theories (2001, background): “However Shipley [ 39, Section 4 ] shows in the context of symmetric spectra that the two de"nitions are equivalent; a proof of the analogous statements in the context of Gamma-rings is similar, but easier.”
Localization theorems in topological Hochschild homology and topological cyclic homology (2008, methodology): “Because of the work of Shipley [33], all technical hypotheses may now be omitted.”
Diagram spaces and symmetric spectra (2011, background): “However, one should keep in mind that GL1 (R) only represents the “correct” homotopy type of the units when R is positive fibrant (or at least semistable in the sense of [38]).”
The Local Structure of Algebraic K-Theory (2012, background): “This poses no real difficulty if we restrict ourselves to the connective case (and allowing some fibrant replacements that were conveniently unnecessary in the Γ-space case, see also [261] and [262] for the non-connective situation), since all the constructions are based on the associated simplicial”
Topological Hochschild homology of Thom spectra and the free loop space (2008, background): “In order to characterize the stable model equivalences in terms of ordinary stable equivalences, Shipley [42] has defined an explicit “detection” functor D : Sp → Sp.”