Algebraic & Geometric Topology

Modular isogeny complexes

Charles Rezk

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We describe a vanishing result on the cohomology of a cochain complex associated to the moduli of chains of finite subgroup schemes on elliptic curves. These results have applications to algebraic topology, in particular to the study of power operations for Morava E–theory at height 2.

Article information

Algebr. Geom. Topol., Volume 12, Number 3 (2012), 1373-1403.

Received: 21 March 2011
Revised: 18 March 2012
Accepted: 10 April 2012
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Secondary: 55N34: Elliptic cohomology 55S25: $K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx] 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22]

power operations elliptic curves Morava E–theory


Rezk, Charles. Modular isogeny complexes. Algebr. Geom. Topol. 12 (2012), no. 3, 1373--1403. doi:10.2140/agt.2012.12.1373.

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