The ℓ-adic Dualizing Complex on an Excellent Surface with Rational Singularities

2008/08/30 by Ting Li, Li, Ting
Mathematics · #14F20 #14J17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14F20 #msc:14J17

paper · pdf · doi:10.48550/arxiv.0809.0068

Totally rewritten. The title is changed.

openalex publication_date 2008/08/30 · arxiv created 2010/04/30 · arxiv updated 2010/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we show that if X is an excellent surface with rational singularities, the constant sheaf ℚ_ℓ is a dualizing complex. In coefficient ℤ_ℓ, we also prove that the obstruction for ℤ_ℓ 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 ℓ-adic cohomology groups on such surfaces.

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