Completed power operations for Morava E–theory

Barthel, Tobias; Frankland, Martin

doi:10.2140/agt.2015.15.2065

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Completed power operations for Morava $E$–theory

Tobias Barthel and Martin Frankland

Algebraic & Geometric Topology 15 (2015) 2065–2131

DOI: 10.2140/agt.2015.15.2065

Abstract

We construct and study an algebraic theory which closely approximates the theory of power operations for Morava $E$ –theory, extending previous work of Charles Rezk in a way that takes completions into account. These algebraic structures are made explicit in the case of $K$ –theory. Methodologically, we emphasize the utility of flat modules in this context, and prove a general version of Lazard’s flatness criterion for module spectra over associative ring spectra.

Keywords

power operation, Morava $E$–theory, Dyer–Lashof, completion, $L$–complete

Mathematical Subject Classification 2010

Primary: 55S25

Secondary: 55S12, 13B35

References

Publication

Received: 7 March 2014

Revised: 16 October 2014

Accepted: 24 November 2014

Published: 10 September 2015

Authors

Tobias Barthel
Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn Germany

Martin Frankland
Department of Mathematics University of Western Ontario Middlesex College London, ON N6A 5B7 Canada

Volume 15, issue 4 (2015)