Towers of MU-algebras and the generalized Hopkins-Miller theorem
Author: A.Lazarev
Department of Mathematics, Univ. of Bristol, Bristol, BS8 1TW,
UK.
email A.Lazarev@bristol.ac.uk
AMS classification number 55N22
Our results are of three types. First we describe a general procedure
of adjoining polynomial variables to A-infinity-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.