The trivial fiber topology and framed motives over the integers

A. Druzhinin; Håkon Kolderup; Paul Arne Østvær

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arXiv · 2012.07365

The trivial fiber topology and framed motives over the integers

A. Druzhinin·Håkon Kolderup·Paul Arne Østvær

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Abstract

This paper introduces the trivial fiber topology on schemes. For one-dimensional base schemes, we use it to describe fibrant replacements in the stable motivic homotopy category and motivic infinite loop spaces. We also extend the Garkusha-Panin and Voevodsky strict $\mathbb{A}^{1}$-invariance theorems to one-dimensional base schemes. The trivial fiber topology plays a central role in the proof of refined localization results for motivic homotopy categories. Moreover, we extend Morel's $\mathbb{A}^{1}$-connectivity theorem on Nisnevich sheaves of stable motivic homotopy groups. These results open new vistas for computations of motivic invariants over deeper base schemes of arithmetic interest.

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BibTeX RIS

A. Druzhinin, Håkon Kolderup, Paul Arne Østvær. 2020-12-14. The trivial fiber topology and framed motives over the integers. https://arxiv.org/abs/2012.07365

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