Volume 15, issue 4 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Completed power operations for Morava $E$–theory

Tobias Barthel and Martin Frankland

Algebraic & Geometric Topology 15 (2015) 2065–2131
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