Local rigid cohomology of singular points

Abstract

We show that if two singular points $x^{\prime }\in X^{\prime }$ and $x\in X$ on schemes over a field $k$ of characteristic $p>0$ are contact equivalent then the rigid cohomology spaces $H_{rig,\{x\}}^{\bullet }(X)$ and $H_{rig,\{x^{\prime }\}}^{\bullet }(X^{\prime })$ are isomorphic. The isomorphism that we construct is moreover compatible with the Frobenius structure on rigid cohomology.

References in corpus (1)

• Orientation theory in arithmetic geometry