Asian Journal of Mathematics
Volume 19 (2015)
Cohomology of rigid curves with semi-stable coverings
Pages: 637 – 650
We construct a semi-stable formal model of a wide open rigid curve with a semi-stable covering, and study the $\ell$-adic cohomology of the rigid curve. We describe the $\ell$-adic cohomology of the rigid curve using the $\ell$-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.
semi-stable covering, rigid analytic curve, cohomology
2010 Mathematics Subject Classification
Primary 11G20. Secondary 14G22.