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Mark Behrens
Buildings, elliptic curves, and the stable homotopy groups of spheres
Abstract:
Fix a prime p. I will describe a dense arithmetic subgroup of the
second Morava stabilizer group at p. This group can be realized as a
group of quasi-endomorphisms of an elliptic curve. It acts naturally
on the Bruhat-Tits building for GL_2(Q_l) for l different than p.
This action has finite stabilizers, which coincide with the
automorphism groups of elliptic curves. The homotopy fixed points of
this group acting on Morava E-theory produces half of the K(2)-local
sphere, and the whole sphere is recovered using Gross-Hopkins duality.
This work generalizes the resolution of Goerss-Henn-Mahowald-Rezk to
all primes.
Some of this work is joint work with Tyler Lawson.
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