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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.
For an equivariant commutative ring spectrum $R$, $pi_0 R$ has algebraic structure reflecting the presence of both additive transfers and multiplicative norms. The additive structure gives rise to a Mackey functor and the multiplicative structure yie
In this paper we prove a Thomason-style descent theorem for the $rho$-complete sphere spectrum. In particular, we deduce a very general etale descent result for torsion, $rho$-complete motivic spectra. To this end, we prove a new convergence result f
We strengthen some results in etale (and real etale) motivic stable homotopy theory, by eliminating finiteness hypotheses, additional localizations and/or extending to spectra from HZ-modules.
Free algebras are always free as modules over the base ring in classical algebra. In equivariant algebra, free incomplete Tambara functors play the role of free algebras and Mackey functors play the role of modules. Surprisingly, free incomplete Tamb
We define a notion of colimit for diagrams in a motivic category indexed by a presheaf of spaces (e.g. an etale classifying space), and we study basic properties of this construction. As a case study, we construct the motivic analogs of the classical