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Several homotopy fixed point spectral sequences in telescopically localized algebraic K-theory
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Description
Let n ≥ 1, p a prime, and T(n) any representative of the Bousfield class of the telescope v−1n F(n) of a finite type n complex. Also, let En be the Lubin-Tate spectrum, K(En) its algebraic K-theory spectrum, and Gn the extended Morava stabilizer group, a profinite group. Motivated by an Ausoni-Rognes conjecture, we show that there are two spectral sequences<br> IEs,t2 ⇒ πt−s((LT(n+1)K(En))hGn) ⇐ IIEs,t2<br> with common abutment π∗(−) of the continuous homotopy fixed points of LT(n+1)K(En), where IEs,t2 is continuous cohomology with coefficients in a certain tower of discrete Gn-modules. If the tower satisfies the Mittag-Leffler condition, then there are isomorphisms with continuous cochain cohomology groups:<br> IE∗,∗2 ≅ H∗cts(Gn, π∗(LT(n+1)K(En))) ≅ IIE∗,∗2.<br> We isolate two hypotheses, the first of which is true when (n, p) = (1, 2), that imply (LT(n+1)K(En))hGn ≃ LT(n+1)K(LK(n)S0). Also, we show that there is a spectral sequence<br> Hscts(Gn, πt(K(En) ⊗ T(n + 1))) ⇒ πt−s((K(En) ⊗ T(n + 1))hGn).
Journal
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- Mathematical Journal of Okayama University
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Mathematical Journal of Okayama University 66 (1), 135-157, 2024-01
Department of Mathematics, Faculty of Science, Okayama University
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Keywords
Details 詳細情報について
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- CRID
- 1390579908258362880
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- NII Book ID
- AA00723502
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- ISSN
- 00301566
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- JaLC
- IRDB