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arXiv · 2511.22560

Real isotropic motivic spectra

Fabio Tanania
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Abstract

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 $\rho$ 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.

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Fabio Tanania. 2025-11-27. Real isotropic motivic spectra. https://arxiv.org/abs/2511.22560

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