Independence of ℓ for the supports in the decomposition theorem

2015/12/31 by Shenghao Sun
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Cohomology #Decomposition #Decomposition theorem #Independence (probability theory) #Intersection (aeronautics) #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.1215/00127094-2017-0059

published as Duke Math. J. 167, no. 10 (2018), 1803-1823 · 15 pages, final version

openalex created_date 2016/06/24 · openalex publication_date 2018/06/13 · arxiv created 2018/08/15 · arxiv updated 2018/08/16 · openalex updated_date 2026/08/05

Abstract

In this article, we prove a result on the independence of ℓ for the supports of irreducible perverse sheaves occurring in the decomposition theorem, as well as for the family of local systems on each support. It generalizes Gabber’s result on the independence of ℓ of intersection cohomology to the relative case.

Citations

• Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil
• Independence of ℓ in Lafforgue's theorem
• Independence of ℓ of monodromy groups
• La conjecture de Weil : II