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arXiv · 1910.01339

A motivic homotopy theory without $\mathbb{A}^1$ invariance

Federico Binda
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Abstract

In this paper, we continue the program initiated by Kahn-Saito-Yamazaki by constructing and studying an unstable motivic homotopy category with modulus, extending the Morel-Voevodsky construction from smooth schemes over a field $k$ to certain diagrams of schemes. We present this category as a candidate environment for studying representability problems for non $\mathbb{A}^1$-invariant generalized cohomology theories.

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Federico Binda. 2019-10-03. A motivic homotopy theory without $\mathbb{A}^1$ invariance. https://doi.org/10.1007/s00209-019-02399-2

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