Journal article 509 views
Framed motivic Gamma-spaces
Grigory Garkusha 
,
Ivan Panin,
Paul Arne Ostvaer
,
Ivan Panin,
Paul Arne Ostvaer
Izvestiya: Mathematics, Volume: 87, Issue: 1, Pages: 1 - 28
Swansea University Author:
Grigory Garkusha
Full text not available from this repository: check for access using links below.
DOI (Published version): 10.4213/im9246e
Abstract
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 Voevodsky’s framed correspondences into the concept of framed motivic Γ-spaces; t...
| Published in: | Izvestiya: Mathematics |
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| ISSN: | 1064-5632 1468-4810 |
| Published: |
Steklov Mathematical Institute
2023
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa60277 |
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| Abstract: |
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 Voevodsky’s framed correspondences into the concept of framed motivic Γ-spaces; these are continuous or enriched functors of two variables that take values in framed motivic spaces. 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, 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 A1-homotopy theory of algebraic varieties. |
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| Keywords: |
Framed correspondences, Γ-spaces, motivic spaces, framed motivic Γ-spaces, connective and very effective motivic spectra, infinite motivic loop spaces. |
| College: |
Faculty of Science and Engineering |
| Issue: |
1 |
| Start Page: |
1 |
| End Page: |
28 |