Transchromatic phenomena in the equivariant slice spectral sequence

2024/03/01 by Lennart Meier, Meier, Lennart, Xiaolin Shi +3 · 3 citations
Mathematics · #Algebraic Topology (math.AT) #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2403.00741

openalex publication_date 2024/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a transchromatic phenomenon for Hill--Hopkins--Ravenel and Lubin--Tate theories. This establishes a direct relationship between the equivariant slice spectral sequences of height-h and height-(h/2) theories. As applications of this transchromatic phenomenon, we prove periodicity and vanishing line results for these theories.

Cited by

• Periodicity and finite complexity in higher real K-theories
• Slice spectral sequences through synthetic spectra
• On higher real K-theories and finite spectra

Related

• The slice spectral sequence of a C₄-equivariant height-4 Lubin-Tate theory
• Periodic phenomena in equivariant stable homotopy theory
• Chromatic defect, Wood's theorem, and higher real K-theories
• Examples of chromatic redshift in algebraic K-theory
• Counterexamples to Hochschild--Kostant--Rosenberg in characteristic p