Algebraic & Geometric Topology

Completed power operations for Morava $E$–theory

Tobias Barthel and Martin Frankland

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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.

Article information

Algebr. Geom. Topol., Volume 15, Number 4 (2015), 2065-2131.

Received: 7 March 2014
Revised: 16 October 2014
Accepted: 24 November 2014
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55S25: $K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]
Secondary: 55S12: Dyer-Lashof operations 13B35: Completion [See also 13J10]

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


Barthel, Tobias; Frankland, Martin. Completed power operations for Morava $E$–theory. Algebr. Geom. Topol. 15 (2015), no. 4, 2065--2131. doi:10.2140/agt.2015.15.2065.

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