homotopy theory (ordinary, equivariant, motivic)
algebraic geometry (ordinary, derived, spectral)
Norms and Transfers in Motivic Homotopy Theory (arXiv)
We study norm functors in the sense of Bachmann--Hoyois for various ∞-categories of correspondences occurring in motivic homotopy theory. We show in particular that the symmetric monoidal structure on the ∞-category of framed correspondence can be refined to a norm monoidal structure, and that the resulting norm monoidal structure on the ∞-category of motivic spectra with framed transfers is compatible with the Reconstruction Theorem of Elmanto--Hoyois--Khan--Sosnilo--Yakerson. This yields a recognition principle for normed motivic spectra. We show similar results for various other flavors of transfer, e.g. finite syntomic and oriented finite Gorenstein.