Results 1 to 10 of about 15,595 (125)
Correspondences and stable homotopy theory [PDF]
Transactions of the London Mathematical Society, 2023 A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra SH is recovered from modules over a commutative symmetric ring ...
Grigory Garkusha
doaj +2 more sources
Rigidity and exotic models for $$v_1$$-local G-equivariant stable homotopy theory [PDF]
Mathematische Zeitschrift, 2017 We prove that the $v_1$-local $G$-equivariant stable homotopy category for $G$ a finite group has a unique $G$-equivariant model at $p=2$. This means that at the prime $2$ the homotopy theory of $G$-spectra up to fixed point equivalences on $K$-theory is
Irakli Patchkoria, Constanze Roitzheim
semanticscholar +3 more sources
A uniqueness theorem for stable homotopy theory [PDF]
, 2000 In this paper we study the global structure of the stable homotopy theory of spectra. We establish criteria for when the homotopy theory associated to a given stable model category agrees with the classical stable homotopy theory of spectra.
S. Schwede, B. Shipley
semanticscholar +6 more sources
Nilpotence and descent in equivariant stable homotopy theory [PDF]
, 2015 Let G be a finite group and let F be a family of subgroups of G. We introduce a class of G-equivariant spectra that we call F -nilpotent. This definition fits into the general theory of torsion, complete, and nilpotent objects in a symmetric monoidal ...
A. Mathew, N. Naumann, J. Noel
semanticscholar +3 more sources
Brown-Peterson spectra in stable A^1-homotopy theory
, 2000 We characterize ring spectra morphisms from the algebraic cobordism spectrum $\QTR{Bbb}{MGL}$ (\QCITE{cite}{}{Vo1}) to an oriented spectrum $\QTR{Bbb}{E}$ (in the sense of Morel \QCITE{cite}{}{Mo}) via formal group laws on the ''topological'' subring $E^{*}=\oplus_iE^{2i,i}$ of $E^{**}$. This result is then used to construct for any prime $p$ a motivic
Vezzosi, Gabriele
openaire +4 more sources
Uniqueness of real ring spectra up to higher homotopy [PDF]
Annals of K-theory, 2023 We discuss a notion of uniqueness up to $n$-homotopy and study examples from stable homotopy theory. In particular, we show that the $q$-expansion map from elliptic cohomology to topological $K$-theory is unique up to $3$-homotopy, away from the prime $2$
J. M. Davies
semanticscholar +1 more source
η$\eta$ ‐Periodic motivic stable homotopy theory over Dedekind domains
Journal of Topology, 2022 We construct well‐behaved extensions of the motivic spectra representing generalized motivic cohomology and connective Balmer–Witt K$K$ ‐theory (among others) to mixed characteristic Dedekind schemes on which 2 is invertible.
Tom Bachmann
semanticscholar +1 more source
The Picard group in equivariant homotopy theory via stable module categories [PDF]
Journal of Topology, 2020 We develop a mechanism of “isotropy separation for compact objects” that explicitly describes an invertible G$G$ ‐spectrum through its collection of geometric fixed points and gluing data located in certain variants of the stable module category.
A. Krause
semanticscholar +1 more source
Proper Equivariant Stable Homotopy Theory [PDF]
Memoirs of the American Mathematical Society, 2019 This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective ‘proper’ alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from equivariant ...
D. Degrijse +4 more
semanticscholar +1 more source
On some adjunctions in equivariant stable homotopy theory [PDF]
, 2018 We investigate certain adjunctions in derived categories of equivariant spectra, including a right adjoint to fixed points, a right adjoint to pullback by an isometry of universes, and a chain of two right adjoints to geometric fixed points.
P. Hu, I. Kríz, P. Somberg
semanticscholar +1 more source