Chromatic homotopy theory is asymptotically algebraic

Tobias Barthel, Tomer M. Schlank, Nathaniel Stapleton

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 languageEnglish
Pages (from-to)737-845
Number of pages109
JournalInventiones Mathematicae
Issue number3
StatePublished - Jun 1 2020

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© 2020, The Author(s).

ASJC Scopus subject areas

  • General Mathematics


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