Chromatic homotopy theory is asymptotically algebraic

Tobias Barthel*, Tomer M. Schlank, Nathaniel Stapleton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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-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.

Original languageAmerican English
Pages (from-to)737-845
Number of pages109
JournalInventiones Mathematicae
Volume220
Issue number3
DOIs
StatePublished - 1 Jun 2020

Bibliographical note

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© 2020, The Author(s).

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