Completed power operations for Morava E–theory

Barthel, Tobias¹ ; Frankland, Martin²

¹Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
²Department of Mathematics, University of Western Ontario, Middlesex College, London, ON N6A 5B7, Canada

Algebraic and Geometric Topology, Tome 15 (2015) no. 4, pp. 2065-2131

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.2065

Classification : 55S25, 55S12, 13B35
Keywords: power operation, Morava $E$–theory, Dyer–Lashof, completion, $L$–complete

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