Buildings, Elliptic Curves, and the K(2)-local Sphere
نویسنده
چکیده
We investigate a dense subgroup Γ of the second Morava stabilizer group given by a certain group of quasi-isogenies of a supersingular elliptic curve in characteristic p. The group Γ acts on the Bruhat-Tits building for GL2(Q`) through its action on the `-adic Tate module. This action has finite stabilizers, giving a small resolution for the homotopy fixed point spectrum (EhΓ 2 ) hGal by spectra of topological modular forms. Here, E2 is a version of Morava E-theory and Gal = Gal(Fp/Fp).
منابع مشابه
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Using degree N isogenies of elliptic curves, we produce a spectrum Q(N). This spectrum is built out of spectra related to tmf . At p = 3 we show that the K(2)local sphere is built out of Q(2) and its K(2)-local Spanier-Whitehead dual. This gives a conceptual reinterpretation a resolution of Goerss, Henn, Mahowald, and Rezk. AMS classification: Primary 55Q40, 55Q51, 55N34. Secondary 55S05, 14H52.
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تاریخ انتشار 2005