Asian Journal of Mathematics

Volume 19 (2015)

Number 4

Cohomology of rigid curves with semi-stable coverings

Pages: 637 – 650



Naoki Imai (Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo, Japan)

Takahiro Tsushima (Department of Mathematics and Informatics, Faculty of Science, Chiba University, Chiba, Japan)


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.

Published 4 November 2015