An algebraic model for rational excisive functors

TL;DR

This paper introduces an algebraic model for rational excisive functors in spectra, providing a new proof of their splitting into homogeneous layers without relying on rational Tate vanishing, by leveraging analogies with equivariant stable homotopy theory.

Contribution

It offers a novel algebraic framework for understanding rational excisive functors, independent of Tate vanishing assumptions, and connects spectra endofunctors with equivariant stable homotopy theory.

Findings

Rational excisive functors split into homogeneous layers algebraically.

New proof of splitting does not depend on rational Tate vanishing.

Establishes an analogy between spectra endofunctors and equivariant stable homotopy theory.

Abstract

We provide a new proof of the rational splitting of excisive endofunctors of spectra as a product of their homogeneous layers independent of rational Tate vanishing. We utilise the analogy between endofunctors of spectra and equivariant stable homotopy theory and as a consequence, we obtain an algebraic model for rational excisive functors.