Completed power operations for Morava E-theory

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.

Version 3: Minor corrections. Journal version, up to small cosmetic changes

References in corpus (3)

• Higher Topos Theory
• Power operations for Morava E-theory of height 2 at the prime 2
• $L$-complete Hopf algebroids and their comodules

Cited by in corpus (11)

• The $E_2$-term of the $K(n)$-local $E_n$-Adams spectral sequence
• Derived completion for comodules
• Centralizers in good groups are good
• Brown-Peterson cohomology from Morava E-theory
• Morava K-theory and Filtrations by Powers
• A user's guide: Completed power operations for Morava $E$-theory
• Power operations in $K$-theory completed at a prime
• Algebraicity in monochromatic homotopy theory
• Localizations of Morava E-theory and deformations of formal groups
• Rational local systems and connected finite loop spaces
• A transchromatic proof of Strickland's theorem