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arXiv · 2604.24888

The $\mathbf{P}^1$-motivic Gysin map

Longke Tang
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Abstract

We develop a $\mathbf{P}^1$-unstable non-$\mathbf{A}^1$-invariant theory of motivic spaces and spectra, and construct the Gysin map therein for regular immersions. This in particular gives the Gysin map in the Annala--Hoyois--Iwasa $\mathbf{P}^1$-motivic spectra, and thus gives a uniform construction for the Gysin maps of various cohomology theories.

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Longke Tang. 2026-04-27. The $\mathbf{P}^1$-motivic Gysin map. https://arxiv.org/abs/2604.24888

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