The $\ell$-adic Dualizing Complex on an Excellent Surface with Rational Singularities

Details The $\ell$-adic Dualizing Complex on an Excellent Surface with Rational Singularities The $\ell$-adic Dualizing Complex on an Excellent Surface with Rational Singularities

2008-08-30

arxiv.org/abs/0809.0068v2

Mathematics

Algebraic Geometry

Totally rewritten. The title is changed.

Scientific paper

In this article, we show that if $X$ is an excellent surface with rational singularities, the constant sheaf $\mathbb{Q}_{\ell}$ is a dualizing complex. In coefficient $\mathbb{Z}_{\ell}$, we also prove that the obstruction for $\mathbb{Z}_{\ell}$ to become a dualizing complex lying on the divisor class groups at singular points. As applications, we study the perverse sheaves and the weights of $\ell$-adic cohomology groups on such surfaces.

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