#### Volume 14, issue 2 (2014)

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The power operation structure on Morava $E\!$–theory of height $2$ at the prime $3$

### Yifei Zhu

Algebraic & Geometric Topology 14 (2014) 953–977
##### Abstract

We give explicit calculations of the algebraic theory of power operations for a specific Morava $E$–theory spectrum and its $K\left(1\right)$–localization. These power operations arise from the universal degree-$3$ isogeny of elliptic curves associated to the $E$–theory.

##### Keywords
power operations, elliptic curves, Morava $E$–theory, $K(1)$–localization
##### Mathematical Subject Classification 2010
Primary: 55S12
Secondary: 55N20, 55N34
##### Publication
Revised: 2 September 2013
Accepted: 10 September 2013
Published: 31 January 2014
##### Authors
 Yifei Zhu Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, IL 60208 USA http://www.math.northwestern.edu/~zyf