Monochromatic homotopy theory is asymptotically algebraic

Abstract

In previous work, we used an $\infty$-categorical version of ultraproducts to show that, for a fixed height $n$, the symmetric monoidal $\infty$-categories of $E_{n,p}$-local spectra are asymptotically algebraic in the prime $p$. In this paper, we prove the analogous result for the symmetric monoidal $\infty$-categories of $K_p(n)$-local spectra, where $K_p(n)$ is Morava $K$-theory at height $n$ and the prime $p$. This requires $\infty$-categorical tools suitable for working with compactly generated symmetric monoidal $\infty$-categories with non-compact unit. The equivalences that we produce here are compatible with the equivalences for the $E_{n,p}$-local $\infty$-categories.

arXiv comment33 pages

References in corpus (6)

• Enriched $\infty$-categories via non-symmetric $\infty$-operads
• The Picard group of topological modular forms via descent theory
• A thick subcategory theorem for modules over certain ring spectra
• Vanishing lines in generalized Adams spectral sequences are generic
• The Chromatic Splitting Conjecture at n=p=2
• On exotic equivalences and a theorem of Franke

Cited by in corpus (7)

• Algebraic K-theory of stable $\infty$-categories via binary complexes
• Separable commutative algebras and Galois theory in stable homotopy theories
• The $\infty$-Categorical Reflection Theorem and Applications
• Morava K-theory and Filtrations by Powers
• Filter Quotients and Non-Presentable $(\infty ,1)$-Toposes
• The higher structure of unstable homotopy groups
• Algebraicity in monochromatic homotopy theory