Framed motivic $\Gamma$-spaces
- Authors: Garkusha G.A.1, Panin I.A.2,3, Østvær P.A.4,3
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Affiliations:
- Swansea University
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
- University of Oslo
- Dipartimento di Matematica "Federigo Enriques", Università degli Studi di Milano
- Issue: Vol 87, No 1 (2023)
- Pages: 3-32
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/142247
- DOI: https://doi.org/10.4213/im9246
- ID: 142247
Cite item
Abstract
We combine several mini miracles to achieve an elementary understandingof infinite loop spaces and very effective spectra in the algebro-geometricsetting of motivic homotopy theory. Our approach combines $\Gamma$-spacesand Voevodsky's framed correspondences into the concept of framed motivic$\Gamma$-spaces; these are continuous or enriched functors of two variablesthat take values in framed motivic spaces. We craft proofs of our mainresults by imposing further axioms on framed motivic $\Gamma$-spacessuch as a Segal condition for simplicial Nisnevich sheaves, cancellation,$\mathbb{A}^1$- and $\sigma$-invariance, Nisnevich excision,Suslin contractibility, and grouplikeness.This adds to the discussion in the literature on coexisting pointsof view on the $\mathbb{A}^1$-homotopy theory of algebraic varieties.
About the authors
Grigory Anatolevich Garkusha
Swansea UniversityDoctor of physico-mathematical sciences, Professor
Ivan Alexandrovich Panin
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences; University of Oslo
Email: paniniv@gmail.com
Doctor of physico-mathematical sciences
Paul Arne Østvær
Dipartimento di Matematica "Federigo Enriques", Università degli Studi di Milano; University of Oslo
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