Obtaining intermediate rings of a local profinite Galois extension without localization

Details Obtaining intermediate rings of a local profinite Galois extension without localization Obtaining intermediate rings of a local profinite Galois extension without localization

2010-06-16

arxiv.org/abs/1006.3288v2

Mathematics

Algebraic Topology

Updated the Acknowledgements and References. This version is accepted for publication in Journal of Homotopy and Related Struc

Scientific paper

Let E_n be the Lubin-Tate spectrum and let G_n be the nth extended Morava stabilizer group. Then there is a discrete G_n-spectrum F_n, with L_{K(n)}(F_n) \simeq E_n, that has the property that (F_n)^{hU} \simeq E_n^{hU}, for every open subgroup U of G_n. In particular, (F_n)^{hG_n} \simeq L_{K(n)}(S^0). More generally, for any closed subgroup H of G_n, there is a discrete H-spectrum Z_{n, H}, such that (Z_{n, H})^{hH} \simeq E_n^{hH}. These conclusions are obtained from results about consistent k-local profinite G-Galois extensions E of finite vcd, where L_k(-) is L_M(L_T(-)), with M a finite spectrum and T smashing. For example, we show that L_k(E^{hH}) \simeq E^{hH}, for every open subgroup H of G.

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