Structured Ring Spectra: Moduli spaces of commutative ring spectra

By Paul G. Goerss, M. Hopkins. 2004

234 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/78f966dab23d8b196c9614823616e887a0c99c95

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Homotopy completion and topological Quillen homology of structured ring spectra (2011, background): “The topological analog for commutative ring spectra, called topological André-Quillen homology, was originally studied by Basterra [6]; see also BakerGilmour-Reinhard [4], Baker-Richter [5], Basterra-Mandell [7, 8], Goerss-Hopkins [25], Lazarev [46], Mandell [52], Richter [62], Rognes [63, 64] and ”
A modular description of the K(2)-local sphere at the prime 3 (2005, methodology): “The Goerss-Hopkins-Miller theorem [40], [ 17 ] states that there is a contravariant functor”
The units of a ring spectrum and a logarithmic cohomology operation (2004, background): “W k is the ring of p-typical Witt vectors on k. Morava E-theory is a 2-periodic complex orientable cohomology theory with as its associat ed formal group; thus π∗E ≈ O[u, u −1 ] with O in degree 0 and u in degree 2. The Hopkins-Miller theorem (see [ GH ],”
Topological modular forms with level structure (2013, background): “The definition of OTate gives a natural map of E∞ ring spectra R → OTate which is an isomorphism on π0, and one of R-modules M → OTate which is an isomorphism on π2.”
Homotopy theory of modules over operads in symmetric spectra (2007, background): “1 Introduction Operads parametrize simple and complicated algebraic structures and naturally arise in several areas of algebraic topology, homotopy theory and homological algebra; see Basterra and Mandell [1], Goerss and Hopkins [13], Hinich and Schechtman [18], Kriz and May [24], May [30] and McClu”
Model Categories and Simplicial Methods (2006, background): “See [ 19 ]. Spectra have not been discussed here, but there is a very rich literature.”
On Hopkins’ Picard groups for the prime 3 and chromatic level 2 (2012, background): “By the Hopkins– Miller–Goerss Theorem [7], this action can be lifted uniquely to E∞-ring spectra; that is, the group Gn acts on the spectrum En through E∞-ring maps.”