Logarithmic Gysin sequences for regular immersions

Doosung Park

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arXiv · 2404.04082

Logarithmic Gysin sequences for regular immersions

Doosung Park

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Abstract

For a regular immersion of schemes $Z\to X$ and a cohomology theory of fs log schemes, we formulate the logarithmic Gysin sequence using the "logarithmic compactification" $(\mathrm{Bl}_Z X,E)$ instead of the open complement $X-Z$, where $E$ is the exceptional divisor. We show that all $\mathbb{A}^1$-invariant cohomology theories produced from motivic spectra and various non $\mathbb{A}^1$-invariant cohomology theories like Nygaard completed prismatic cohomology admit logarithmic Gysin sequences.

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Doosung Park. 2024-04-05. Logarithmic Gysin sequences for regular immersions. https://arxiv.org/abs/2404.04082

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