Motivic Tambara Functors

TL;DR

This paper characterizes the category of normed motivic spectra over a field as sheaves with transfers and étale norms, revealing a deep connection to classical Tambara functors in motivic homotopy theory.

Contribution

It provides an explicit description of normed motivic spectra as sheaves with generalized transfers and étale norms, linking motivic homotopy theory to Tambara functors.

Findings

Explicit description of NAlg(HI_0(k)) as sheaves with transfers and étale norms

Connection established between motivic spectra and classical Tambara functors

Enhanced understanding of the structure of effective homotopy modules

Abstract

Let k be a field and denote by SH(k) the motivic stable homotopy category. Recall its full subcategory HI_0(k) of effective homotopy modules. Write NAlg(HI_0(k)) for the category of normed motivic spectra with underlying spectrum an effective homotopy module. In this article we provide an explicit description of NAlg(HI_0(k)) as the category of sheaves with generalized transfers and \'etale norms, and explain how this is closely related to the classical notion of Tambara functors.