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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 484, Pages 59–71
(Mi znsl6856)
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Smooth affine model for the framed correspondences spectrum
A. E. Druzhininab a Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Abstract:
The framed correspondences $T$-spectrum of a smooth affine scheme is a $T$-spectrum of Nisnevich sheaves. We construct the motivically equivalent model of the $T$-spectrum representable in the category of pairs of smooth affine ind-schemes in the case of a base scheme of a finite Krull dimension. In other words, the motivic spaces of $(\mathbb{P},\infty)^{\wedge \infty}$-loops in the relative motivic sphere $\mathbb{A}_Y^{\infty+l}/(\mathbb{A}_Y^{\infty+l}-0)$ are represented in the category of pairs of smooth affine ind-schemes. The construction in not functorial on the category of smooth affine schemes, but it is so on the category of smooth affine framed schemes, that is defined in the text.
Key words and phrases:
loop spaces, smooth models, stably motivically fibrant spectra, framed correspondences.
Received: 25.11.2019
Citation:
A. E. Druzhinin, “Smooth affine model for the framed correspondences spectrum”, Problems in the theory of representations of algebras and groups. Part 35, Zap. Nauchn. Sem. POMI, 484, POMI, St. Petersburg, 2019, 59–71
Linking options:
https://www.mathnet.ru/eng/znsl6856 https://www.mathnet.ru/eng/znsl/v484/p59
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Abstract page: | 73 | Full-text PDF : | 23 | References: | 10 |
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