Equivariant Orthogonal Spectra and S-Modules

By Michael A. Mandell, Jon P. May. 2002

380 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9388c993beb550aca5d0b2dcc39db22ab7c2edc1

How researchers see this paper

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

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

The spectrum of the equivariant stable homotopy category of a finite group (2015, background): “, the Lewis–May approach to G-spectra [22], but more recent foundations such as equivariant orthogonal spectra [23] would serve equally well.”
Traces in symmetric monoidal categories (2011, background): “(Actually, there are many such categories Sp, all equivalent up to homotopy, but each having different technical advantages and disadvantages; see for instance [13, 28, 29].”
On the nonexistence of elements of Kervaire invariant one (2009, methodology): “To meet these demands, we will use as foundations the theory of equivariant orthogonal spectra [22, 21].”
The homotopy theory of cyclotomic spectra (2013, methodology): “Following [8], we omit notation for the forgetful functor from orthogonal T–spectra to non-equivariant orthogonal spectra.”
Model Categories of Diagram Spectra (2001, methodology): “In [36] and [ 24 ], the approach to stable homotopy theory based on diagram categories is compared to the approach based on classical spectra with additional structure of [11].”
Stable model categories are categories of modules (2003, background): “In [37], G-equivariant orthogonal spectra are shown to form a cofibrantly generated, topological (hence simplicial), proper model category (the monoidal structure plays no role for our present considerations).”
Equivariant Universal Coefficient and Künneth Spectral Sequences (2004, background): “Note that since the model categories in [5, 11, 12] are simplicial and the objects M̄s−1 and M are cofibrant, these are cofibrant objects and are cofibers in the sense of Quillen.”
The C2–spectrum Tmf1(3) and its invertible modules (2015, background): “These were introduced by Mandell-May [MM02], though we draw heavily from [HHR09] and also recommend [Sch14] for a slightly different point of view on the same subject matter.”
Spectral Mackey functors and equivariant algebraic K-theory (I) (2014, methodology): “When G is finite, it follows from work of Bert Guillou and Peter May [13] that the homotopy theory of spectral Mackey functors is equivalent to the homotopy theory of G-equivariant spectra in the sense of Lewis–May–Steinberger [25], Mandell–May [33], and Hill–Hopkins–Ravenel [15, 17, 16].”
On the de Rham–Witt complex in mixed characteristic (2004, methodology): “The model category we use is the category of symmetric spectra in the category of orthogonalT-spectra, [20].”
Models of G–spectra as presheaves of spectra (2011, background): “py category with its attendant model structures takes a fair amount of work. The original version was due to Lewis and May [19], and details of more modern versions have been given by Mandell and May [20, 23, 29]. Most of these sources work with compact Lie groups of equivariance. A result of Schwed”
Categorical Homotopy Theory (2014, background): “When G is a finite group, orthogonal G-spectra are most concisely defined to be Top∗ -enriched diagrams on a particular Top∗ -enriched category IG taking values in (Top ∗ )G [MM02].”