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arXiv · 1109.2824

Cohomology of rigid curves with semi-stable coverings

Naoki Imai·Takahiro Tsushima
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Abstract

We construct a semi-stable formal model of a wide open rigid curve with a semi-stable covering, and study the l-adic cohomology of the rigid curve. We describe the l-adic cohomology of the rigid curve using the l-adic cohomology of the irreducible components of a semi-stable reduction, and homology and cohomology of some graphs. We also prove the functoriality of the description for a finite flat morphism that is compatible with semi-stable coverings of wide open rigid curves.

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Naoki Imai, Takahiro Tsushima. 2011-09-13. Cohomology of rigid curves with semi-stable coverings. https://doi.org/10.4310/ajm.2015.v19.n4.a3

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