scholarly journals Topological Hochschild homology and the cyclic bar construction in symmetric spectra

2016 ◽  
Vol 144 (9) ◽  
pp. 4099-4106 ◽  
Author(s):  
Irakli Patchkoria ◽  
Steffen Sagave
Keyword(s):  
Hochschild Homology ◽  
Symmetric Spectra ◽  
Bar Construction ◽  
Topological Hochschild Homology

scholarly journals Towards an understanding of ramified extensions of structured ring spectra

2018 ◽  
Vol 168 (3) ◽  
pp. 435-454 ◽  
Author(s):  
BJØRN IAN DUNDAS ◽  
AYELET LINDENSTRAUSS ◽  
BIRGIT RICHTER
Keyword(s):  
Hochschild Homology ◽  
Second Order ◽  
Ring Spectra ◽  
Quotient Maps ◽  
Local Complex ◽  
K Theory ◽  
Tame Ramification ◽  
Topological Hochschild Homology

AbstractWe propose topological Hochschild homology as a tool for measuring ramification of maps of structured ring spectra. We determine second order topological Hochschild homology of the p-local integers. For the tamely ramified extension of the map from the connective Adams summand to p-local complex topological K-theory we determine the relative topological Hochschild homology and show that it detects the tame ramification of this extension. We show that the complexification map from connective topological real to complex K-theory shows features of a wildly ramified extension. We also determine relative topological Hochschild homology for some quotient maps with commutative quotients.

Topological Hochschild homology and integral p $p$ -adic Hodge theory

2019 ◽  
Vol 129 (1) ◽  
pp. 199-310 ◽  
Author(s):  
Bhargav Bhatt ◽  
Matthew Morrow ◽  
Peter Scholze
Keyword(s):  
Hodge Theory ◽  
Hochschild Homology ◽  
Topological Hochschild Homology

On the Topological Hochschild Homology of bu, I

1993 ◽  
Vol 115 (1) ◽  
pp. 1 ◽  
Author(s):  
J. E. McClure ◽  
R. E. Staffeldt
Keyword(s):  
Hochschild Homology ◽  
Topological Hochschild Homology
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