scholarly journals Relative algebraic K-theory and topological cyclic homology

1997 ◽  
Vol 179 (2) ◽  
pp. 197-222 ◽  
Author(s):  
Randy McCarthy
Keyword(s):  
Cyclic Homology ◽  
Topological Cyclic Homology ◽  
K Theory

scholarly journals $K$-theory and topological cyclic homology of Henselian pairs

2020 ◽  
pp. 1
Author(s):  
Dustin Clausen ◽  
Akhil Mathew ◽  
Matthew Morrow
Keyword(s):  
Cyclic Homology ◽  
Topological Cyclic Homology ◽  
K Theory

scholarly journals Relative K-theory and topological cyclic homology

1997 ◽  
Vol 179 (2) ◽  
pp. 223-242 ◽  
Author(s):  
Bjørn Ian Dundas
Keyword(s):  
Cyclic Homology ◽  
Topological Cyclic Homology ◽  
K Theory

scholarly journals Bi-relative algebraic K-theory and topological cyclic homology

2006 ◽  
Vol 166 (2) ◽  
pp. 359-395 ◽  
Author(s):  
Thomas Geisser ◽  
Lars Hesselholt
Keyword(s):  
Cyclic Homology ◽  
Topological Cyclic Homology ◽  
K Theory

scholarly journals Pro unitality and pro excision in algebraic K-theory and cyclic homology

2018 ◽  
Vol 2018 (736) ◽  
pp. 95-139 ◽  
Author(s):  
Matthew Morrow
Keyword(s):  
Short Proof ◽  
Hochschild Homology ◽  
Cyclic Homology ◽  
Strong Form ◽  
Noetherian Rings ◽  
General Base ◽  
Continuity Properties ◽  
Suitable Sense ◽  
K Theory

AbstractThe purpose of this paper is to study pro excision in algebraicK-theory and cyclic homology, after Suslin–Wodzicki, Cuntz–Quillen, Cortiñas, and Geisser–Hesselholt, as well as continuity properties of André–Quillen and Hochschild homology. A key tool is first to establish the equivalence of various pro Tor vanishing conditions which appear in the literature.This allows us to prove that all ideals of commutative, Noetherian rings are pro unital in a suitable sense. We show moreover that such pro unital ideals satisfy pro excision in derived Hochschild and cyclic homology. It follows hence, and from the Suslin–Wodzicki criterion, that ideals of commutative, Noetherian rings satisfy pro excision in derived Hochschild and cyclic homology, and in algebraicK-theory.In addition, our techniques yield a strong form of the pro Hochschild–Kostant–Rosenberg theorem; an extension to general base rings of the Cuntz–Quillen excision theorem in periodic cyclic homology; a generalisation of the Feĭgin–Tsygan theorem; a short proof of pro excision in topological Hochschild and cyclic homology; and new Artin–Rees and continuity statements in André–Quillen and Hochschild homology.

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