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  Chromatic homotopy theory is asymptotically algebraic

Barthel, T., Schlank, T. M., & Stapleton, N. (2020). Chromatic homotopy theory is asymptotically algebraic. Inventiones mathematicae, 220(3), 737-845. doi:10.1007/s00222-019-00943-9.

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Barthel-Schlank-Stapleton_Chromatic homotopy theory_2020.pdf (Publisher version), 773KB
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Barthel-Schlank-Stapleton_Chromatic homotopy theory_2020.pdf
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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https://doi.org/10.1007/s00222-019-00943-9 (Publisher version)
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 Creators:
Barthel, Tobias1, Author           
Schlank, Tomer M.1, Author           
Stapleton, Nathaniel1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Topology, Mathematics, Category Theory
 Abstract: Inspired 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-prinicipal 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.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
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 Rev. Type: Peer
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Title: Inventiones mathematicae
  Abbreviation : Invent. math.
Source Genre: Journal
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Pages: - Volume / Issue: 220 (3) Sequence Number: - Start / End Page: 737 - 845 Identifier: -