Author:A.Lazarev

Title: Homotopy theory of A-infinity ring spectra and applications to
MU-modules.

To appear in K-theory

Department of Mathematics, Univ. of Bristol, Bristol, BS8 1TW, UK. 


Abstract.
We give a definition of a derivation of an A-infinity ring spectrum
 and relate this notion to
topological Hochschild cohomology. Strict multiplicative
structure is introduced
 into Postnikov towers and generalized Adams towers of A-inifinity-ring spectra.
An obstruction theory for lifting multiplicative maps is constructed.
The developed techniques are then applied to show that a broad class 
of complex-oriented spectra admit structures of MU-algebras where MU 
is the complex cobordism spectrum. Various 
computations of topological derivations and topological Hochschild 
cohomology are made.