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The congruence criterion for power operations in Morava E-theory

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arxiv 0902.2499 v2 pith:AXLXT5HA submitted 2009-02-14 math.AT

Charles Rezk This is my paper · ORCID
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keywords congruencecriterione-theorymoravaoperationspoweradditionalgebraic
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We prove a congruence criterion for the algebraic theory of power operations in Morava E-theory, analogous to Wilkerson's congruence criterion for torsion free lambda-rings. In addition, we provide a geometric description of this congruence criterion, in terms of sheaves on the moduli problem of deformations of formal groups and Frobenius isogenies.

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  1. Level structures and cyclic power operations on the homology of $\mathbb{E}_\infty$ spaces

    math.AT 2026-07 conditional novelty 5.0 of 10

    New explicit formulas for the additive C_2 power operations on the indecomposables of KU_0(BU), E_2[BU], and E_2[BSU] modulo decomposables, derived from the level-structure interpretation of power operations.

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