2 3 A pr 2 00 9 On the Tate spectrum of tmf at the prime 2
نویسنده
چکیده
Computations involving the so-called root invariant prompted Mahowald and Shick to develop the slogan: “the root invariant of vn-periodic homotopy is vn-torsion.” While neither a proof, nor a precise statement, of this slogan appears in the literature numerous authors have offered computational evidence lending further credence toward its truth. The root invariant is closely related to Mahowald’s inverse limit construction of the Tate spectrum. Computations have shown the Tate spectrum of vn-periodic cohomology theories are vn-torsion. The purpose of this paper is to split the Tate spectrum of tmf as a wedge of suspensions of bo, providing yet another example to the literature.
منابع مشابه
A ug 2 00 5 A modular description of the K ( 2 ) - local sphere at the prime 3
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.
متن کاملul 2 00 5 A modular description of the K ( 2 ) - local sphere at the prime 3
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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