## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 11, Number 2 (2009), 327-379.

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

#### 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.

#### Article information

**Source**

Homology Homotopy Appl., Volume 11, Number 2 (2009), 327-379.

**Dates**

First available in Project Euclid: 27 January 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1296138524

**Mathematical Reviews number (MathSciNet)**

MR2591924

**Zentralblatt MATH identifier**

1193.55010

**Subjects**

Primary: 55S25: $K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx] 55S12: Dyer-Lashof operations 14L05: Formal groups, $p$-divisible groups [See also 55N22]

**Keywords**

Power operation Morava E-theory

#### Citation

Rezk, Charles. The congruence criterion for power operations in Morava E-theory. Homology Homotopy Appl. 11 (2009), no. 2, 327--379. https://projecteuclid.org/euclid.hha/1296138524