Buildings, elliptic curves, and the K(2)-local sphere

2005/10/03 by Behrens, Mark · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0510026

Abstract

We investigate a dense subgroup Gamma of the second Morava stabilizer group given by a certain group of quasi-isogenies of a supersingular elliptic curve in characteristic p. The group Gamma acts on the Bruhat-Tits building for GL₂(Q_l) through its action on the l-adic Tate module. This action has finite stabilizers, giving a small resolution for the homotopy fixed point spectrum (E₂^hGamma)^hGal by spectra of topological modular forms. Here, E₂ is a version of Morava E-theory and Gal = Gal(barF_p/F_p).

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• Revisiting the β₁-action on the 3-primary stable homotopy groups of spheres

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• Topological automorphic forms
• Cohomology of the Morava stabilizer group through the duality resolution at n=p=2
• A modular description of the K(2)-local sphere at the prime 3
• Power Operations on K(n-1)-Localized Morava E-theory at Height n