Geometric models for fibrant resolutions of motivic suspension spectra

Andrei Druzhinin

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arXiv · 1811.11086

Geometric models for fibrant resolutions of motivic suspension spectra

Andrei Druzhinin

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Abstract

We construct geometric models for the $\mathbb P^1$-spectrum $M_{\mathbb P^1}(Y)$, which computes in Garkusha-Panin's theory of framed motives \cite{GP14} a positively motivically fibrant $\Omega_{\mathbb P^1}$ replacement of $\Sigma_{\mathbb P^1}^\infty Y$ for a smooth scheme $Y\in \Sm_k$ over a perfect field $k$. Namely, we get the $T$-spectrum in the category of pairs of smooth ind-schemes that defines $\mathbb P^1$-spectrum of pointed sheaves termwise motivically equivalent to $M_{\mathbb P^1}(Y)$.

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Andrei Druzhinin. 2018-11-27. Geometric models for fibrant resolutions of motivic suspension spectra. https://arxiv.org/abs/1811.11086

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