Real isotropic motivic spectra
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909964187992064 |
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| author | Tanania, Fabio |
| author_facet | Tanania, Fabio |
| contents | In this paper, we introduce the category of real isotropic motivic spectra, and show that the real realization functor from motivic spectra over $\mathbb{R}$ to classical spectra factors through it. We then describe its cellular subcategory as a one-parameter deformation of the category of spectra, with parameter $ρ$ corresponding to $-1 \in \mathbb{R}^{\times}$, whose special fiber is the derived category of comodules over the dual Steenrod algebra. This leads to an identification of real isotropic cellular spectra with $\mathbb{F}_2$-synthetic spectra, and sheds light on the relation between motivic homotopy theory over $\mathbb{R}$ and $\mathbb{F}_2$-synthetic homotopy theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Real isotropic motivic spectra Tanania, Fabio Algebraic Geometry Algebraic Topology In this paper, we introduce the category of real isotropic motivic spectra, and show that the real realization functor from motivic spectra over $\mathbb{R}$ to classical spectra factors through it. We then describe its cellular subcategory as a one-parameter deformation of the category of spectra, with parameter $ρ$ corresponding to $-1 \in \mathbb{R}^{\times}$, whose special fiber is the derived category of comodules over the dual Steenrod algebra. This leads to an identification of real isotropic cellular spectra with $\mathbb{F}_2$-synthetic spectra, and sheds light on the relation between motivic homotopy theory over $\mathbb{R}$ and $\mathbb{F}_2$-synthetic homotopy theory. |
| title | Real isotropic motivic spectra |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2511.22560 |