# Enchiridion: Vol. 2 (2016): Martin Frankland

Author
Martin Frankland (Universität Osnabrück)

Source Paper
Completed power operations for Morava $E$-theory
joint with Tobias Barthel
(arxiv:1311.7123)

Source Paper 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.