Motivic Tambara Functors

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 étale norms, and explain how this is closely related to the classical notion of Tambara functors.

v2: version accepted for publication. 20 pages; comments always welcome

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• Higher Topos Theory
• Motivic and Real Etale Stable Homotopy Theory
• The Generalized Slices of Hermitian K-Theory
• On the effectivity of spectra representing motivic cohomology theories
• MW-motivic complexes
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Cited by in corpus (2)

• MW-homotopy sheaves and Morel generalized transfers
• Towards conservativity of ${\mathbb{G}}_m$-stabilization