Chromatic Higher Semiadditivity by Height Induction

TL;DR

This paper presents a novel proof of the chromatic higher semiadditivity of $K(n)$-local spectra, using height induction and algebraic K-theory, advancing understanding in chromatic homotopy theory.

Contribution

It introduces a new proof method for $ $-semiadditivity that avoids traditional computations, leveraging recent developments in chromatic homotopy theory and the redshift conjecture.

Findings

Proof of $ $-semiadditivity via height induction

Utilizes algebraic K-theory and recent chromatic advances

Avoids classical Morava K-theory computations

Abstract

We give a new proof of the $\infty$-semiadditivity of $K(n)$-local spectra. The proof proceeds by induction on the height via algebraic K-theory, utilizing recent advances in chromatic homotopy theory and the redshift conjecture, instead of using the Ravenel-Wilson computation of the Morava K-theory of Eilenberg-MacLane spaces.