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We describe a special instance of the Goerss-Hopkins obstruction theory, due to Senger, for calculating the moduli of $E_infty$ ring spectra with given mod-$p$ homology. In particular, for the $2$-primary Brown-Peterson spectrum we give a chain complex that calculates the first obstruction groups, locate the first potential genuine obstructions, and discuss how some of the obstruction classes can be interpreted in terms of secondary operations.
We extend the Bousfield-Kan spectral sequence for the computation of the homotopy groups of the space of minimal A-infinity algebra structures on a graded projective module. We use the new part to define obstructions to the extension of truncated min
In this paper we develop methods for classifying Baker-Richter-Szymiks Azumaya algebras over a commutative ring spectrum, especially in the largely inaccessible case where the ring is nonconnective. We give obstruction-theoretic tools, constructing a
In this survey paper on commutative ring spectra we present some basic features of commutative ring spectra and discuss model category structures. As a first interesting class of examples of such ring spectra we focus on (commutative) algebra spectra
We review and extend the theory of Thom spectra and the associated obstruction theory for orientations. We recall (from May, Quinn, and Ray) that a commutative ring spectrum A has a spectrum of units gl(A). To a map of spectra f: b -> bgl(A), we asso
Ramification for commutative ring spectra can be detected by relative topological Hochschild homology and by topological Andre-Quillen homology. In the classical algebraic context it is important to distinguish between tame and wild ramification. Noe