A nilpotent Whitehead theorem for $\mathsf{TQ}$-homology of structured ring spectra

2018 ◽  
Vol 11 (3) ◽  
pp. 69-79
Author(s):  
Michael Ching ◽  
John E. Harper
Keyword(s):  
Ring Spectra

scholarly journals Ring spectra which are Thom complexes

1979 ◽  
Vol 46 (3) ◽  
pp. 549-559 ◽  
Author(s):  
Mark Mahowald
Keyword(s):  
Ring Spectra

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.

Commutative 2-local ring spectra

1997 ◽  
Vol 127 (1) ◽  
pp. 1-10 ◽  
Author(s):  
L. Astey
Keyword(s):  
Local Ring ◽  
Simple Proof ◽  
Ring Spectra ◽  
Related Theorem

A theorem is proved characterising representable, multiplicative commutative cohomology theories that split as sums of singular cohomologies after localisation at 2. This theorem is shown to be equivalent to one proved by Würgler and Pazhitnov and Rudyak, for which we provide a simplified proof. We also provide a simple proof of a related theorem of Boardman.

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