The ℓ-adic dualizing complex on an excellent surface with rational singularities

Abstract

In this article, we show that if X is an excellent surface with rational singularities, the constant sheaf ℚl is a dualizing complex. In coefficient ℤl, we also prove that the obstruction for ℤl to become a dualizing complex, lies on the divisor class groups at singular points. As applications, we study the perverse sheaves and the weights of l-adic cohomology groups on such surfaces.