Cohomology of rigid curve with semi-stable covering

Details Cohomology of rigid curve with semi-stable covering Cohomology of rigid curve with semi-stable covering

2011-09-13

arxiv.org/abs/1109.2824v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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 functoriarity of the description for a finite flat morphism that is compatible with semi-stable coverings of wide open rigid curves.

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