2019/06/30 by Grigory Garkusha, Garkusha, Grigory, Ivan Panin +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1907.00433
openalex publication_date 2019/06/30 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines Γ-spaces and framed correspondences into the concept of framed motivic Γ-spaces; these are continuous or enriched functors of two variables that take values in motivic spaces and are equipped with a framing. We craft proofs of our main results by imposing further axioms on framed motivic Γ-spaces such as a Segal condition for simplicial Nisnevich sheaves, cancellation, \mathbb A1- and σ-invariance, Nisnevich excision, Suslin contractibility, and grouplikeness. This adds to the discussion in the literature on coexisting points of view on the \mathbb A1-homotopy theory of algebraic varieties.