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Towards an understanding of ramified extensions of structured ring spectra

Published online by Cambridge University Press:  25 March 2018

BJØRN IAN DUNDAS ,
AYELET LINDENSTRAUSS  and
BIRGIT RICHTER
BJØRN IAN DUNDAS
Affiliation:
Department of Mathematics, University of Bergen, Postboks 7800, 5020 Bergen, Norway. e-mail: dundas@math.uib.no
AYELET LINDENSTRAUSS
Affiliation:
Mathematics Department, Indiana University, 831 East Third Street Bloomington, IN 47405, U.S.A., e-mail: alindens@indiana.edu
BIRGIT RICHTER
Affiliation:
Fachbereich Mathematik der Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany. e-mail: birgit.richter@uni-hamburg.de
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Abstract

We 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 3 , May 2020 , pp. 435 - 454
Copyright
Copyright © Cambridge Philosophical Society 2018

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