Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

The congruence criterion for power operations in Morava $E$-theory

Pages: 327 – 379

DOI: https://dx.doi.org/10.4310/HHA.2009.v11.n2.a16

Author

Charles Rezk (Department of Mathematics, University of Illinois, Urbana, Il., U.S.A.)

Abstract

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 λ-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.

Keywords

power operation, Morava E-theory

2010 Mathematics Subject Classification

14L05, 55S12, 55S25

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Published 1 January 2009