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Logarithmic Gysin sequences for regular immersions
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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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The logarithmic $h$- and $v$-topologies
The paper defines log h- and v-topologies, identifies log v-covers with universally subtrusive morphisms, and proves lv-descent for log étale cohomology with torsion coefficients.
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