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

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

2005-10-03

arxiv.org/abs/math/0510026v1

Mathematics

Algebraic Topology

41 pages

Scientific paper

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 GL_2(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 (E_2^hGamma)^hGal by spectra of topological modular forms. Here, E_2 is a version of Morava E-theory and Gal = Gal(barF_p/F_p).

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