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

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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.

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Authors and Affiliations

  1. Mathematical College, Sichuan University, Chengdu, 610064, P. R. China

    Ting Li

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  1. Ting Li
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Correspondence to Ting Li.

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Supported by National Natural Science Foundation of China (Grant No. 10626036)

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Li, T. The ℓ-adic dualizing complex on an excellent surface with rational singularities. Acta. Math. Sin.-English Ser. 28, 1559–1574 (2012). https://doi.org/10.1007/s10114-012-1002-6

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  • DOI: https://doi.org/10.1007/s10114-012-1002-6

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