The $\mathbf{P}^1$-motivic Gysin map
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913066898161664 |
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| author | Tang, Longke |
| author_facet | Tang, Longke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $\mathbf{P}^1$-motivic Gysin map Tang, Longke Algebraic Geometry Algebraic Topology K-Theory and Homology 14F42 (Primary) 19E15, 14C25 (Secondary) 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. |
| title | The $\mathbf{P}^1$-motivic Gysin map |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology 14F42 (Primary) 19E15, 14C25 (Secondary) |
| url | https://arxiv.org/abs/2604.24888 |