Rings, Modules, and Algebras in Stable Homotopy Theory

By A. Elmendorf, Michael Cole. 2007

704 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/e6d4c84648a0c5d0f5ec229c8e0e7f70badb9e1d

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Citations in the corpus

Derived Algebraic Geometry (2014, neutral): “27 2.6 Derived geometry in other contexts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31”
What precisely are E∞ring spaces and E∞ring spectra? (2009, methodology): “There is an analogous comparison of I -FCP’s and L -spaces, although this has not yet appeared in print, In essence, it mimics the spectrum level constructions of [19] on the space level.”
Equivariant iterated loop space theory and permutative G–categories (2012, methodology): “As in [12], we let S , Sp, and Z denote the categories of orthogonal spectra [21], Lewis-May spectra [19], and EKMM S-modules [8].”
Rings, modules, and algebras in infinite loop space theory (2004, methodology): “The motivation comes from the new tools provided by the modern categories of spectra such as those of [5] and [7], which provide cleaner versions of old questions as well as new ones that could not be asked before.”
Brauer groups and étale cohomology in derived algebraic geometry (2012, background): “from the long exact sequence in homology. Consider the Tor spectral sequence E2 p,q = Tor π∗R p (π∗P,π0R)q ⇒πp+q(P ⊗R π0R) = Hp+q(P ⊗R π0R) with diﬀerentials dr p,q of degree (−r,r −1) constructed in [EKMM97]. If P is a non-trivial perfect R-module with Tor-amplitude contained in [0,b], then the abu”
A Guide for Computing Stable Homotopy Groups (2018, background): “atments of diﬀerent modern models of the category of spectra together with all of its structure, see the ﬁrst parts of Schwede [Sch], Mandell–May–Schwede–Shipley [MMSS01], Elmendorﬀ– Kriz–Mandell–May [EKMM97] or Lurie [Lur]. For the equivariant treatment, see Lewis–May–Steinberger [LMSM86]. Notation”