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arXiv · 0809.0068

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

Ting Li
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Abstract

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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Ting Li. 2010-04-30. The $\ell$-adic Dualizing Complex on an Excellent Surface with Rational Singularities. https://arxiv.org/abs/0809.0068

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