scholarly journals Algebraic chromatic homotopy theory for BP∗BP-comodules

2018 ◽  
Vol 117 (6) ◽  
pp. 1135-1180 ◽  
Author(s):  
Tobias Barthel ◽  
Drew Heard
Keyword(s):  
Homotopy Theory ◽  
Chromatic Homotopy

scholarly journals Affineness and chromatic homotopy theory

2015 ◽  
Vol 8 (2) ◽  
pp. 476-528 ◽  
Author(s):  
Akhil Mathew ◽  
Lennart Meier
Keyword(s):  
Homotopy Theory ◽  
Chromatic Homotopy

scholarly journals Chromatic homotopy theory is asymptotically algebraic

2020 ◽  
Vol 220 (3) ◽  
pp. 737-845
Author(s):  
Tobias Barthel ◽  
Tomer M. Schlank ◽  
Nathaniel Stapleton
Keyword(s):  
Asymptotic Solution ◽  
Homotopy Theory ◽  
Approximation Problem ◽  
Prime Numbers ◽  
Isomorphism Theorem ◽  
Mathematical Objects ◽  
Infinite Collection ◽  
Chromatic Homotopy

AbstractInspired by the Ax–Kochen isomorphism theorem, we develop a notion of categorical ultraproducts to capture the generic behavior of an infinite collection of mathematical objects. We employ this theory to give an asymptotic solution to the approximation problem in chromatic homotopy theory. More precisely, we show that the ultraproduct of the E(n, p)-local categories over any non-principal ultrafilter on the set of prime numbers is equivalent to the ultraproduct of certain algebraic categories introduced by Franke. This shows that chromatic homotopy theory at a fixed height is asymptotically algebraic.

Equivariant Topology and Derived Algebra

2021 ◽  
Keyword(s):  
Homotopy Theory ◽  
Algebraic Models ◽  
Research Papers ◽  
Model Categories ◽  
Homotopy Limits ◽  
Equivariant Topology ◽  
Mackey Functors ◽  
Chromatic Homotopy ◽  
Equivariant Spectra ◽  
Bousfield Localization

This volume contains eight research papers inspired by the 2019 'Equivariant Topology and Derived Algebra' conference, held at the Norwegian University of Science and Technology, Trondheim in honour of Professor J. P. C. Greenlees' 60th birthday. These papers, written by experts in the field, are intended to introduce complex topics from equivariant topology and derived algebra while also presenting novel research. As such this book is suitable for new researchers in the area and provides an excellent reference for established researchers. The inter-connected topics of the volume include: algebraic models for rational equivariant spectra; dualities and fracture theorems in chromatic homotopy theory; duality and stratification in tensor triangulated geometry; Mackey functors, Tambara functors and connections to axiomatic representation theory; homotopy limits and monoidal Bousfield localization of model categories.

On equivariant disconnected rational homotopy theory

2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński
Keyword(s):  
Homotopy Theory ◽  
Weak Equivalence ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Hamiltonian Group ◽  
Simplicial Set ◽  
De Rham

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

scholarly journals A First Approximation to Homotopy Theory

1953 ◽  
Vol 39 (7) ◽  
pp. 655-660 ◽  
Author(s):  
E. H. Spanier ◽  
J. H. C. Whitehead
Keyword(s):  
Homotopy Theory ◽  
First Approximation
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