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Towers of MU ‐Algebras and the Generalized Hopkins–Miller theorem
Author(s) -
Lazarev A.
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014102
Subject(s) - mathematics , multiplicative function , spectrum (functional analysis) , context (archaeology) , polynomial , ring (chemistry) , ideal (ethics) , homotopy , polynomial ring , pure mathematics , algebraic number , mathematical analysis , biology , paleontology , philosophy , chemistry , physics , organic chemistry , epistemology , quantum mechanics
Our results are of three types. First, we describe a general procedure of adjoining polynomial variables to A ∞ ‐ring spectra whose coefficient rings satisfy certain restrictions. A host of examples of such spectra is provided by killing a regular ideal in the coefficient ring of MU , the complex cobordism spectrum. Second, we show that the algebraic procedure of adjoining roots of unity carries over in the topological context for such spectra. Third, we use the developed technology to compute the homotopy types of spaces of strictly multiplicative maps between suitable K ( n )‐localizations of such spectra. This generalizes the famous Hopkins–Miller theorem and gives strengthened versions of various splitting theorems. 2000 Mathematics Subject Classification 55N20, 55S35, 55T25 (primary), 16E40, 13D10 (secondary).