Duke Mathematical Journal

Independence of for the supports in the decomposition theorem

Shenghao Sun

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this article, we prove a result on the independence of 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 of intersection cohomology to the relative case.

Article information

Source
Duke Math. J., Volume 167, Number 10 (2018), 1803-1823.

Dates
Received: 30 November 2015
Revised: 3 May 2017
First available in Project Euclid: 13 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1528855662

Digital Object Identifier
doi:10.1215/00127094-2017-0059

Mathematical Reviews number (MathSciNet)
MR3827811

Zentralblatt MATH identifier
06928111

Subjects
Primary: 14F20: Étale and other Grothendieck topologies and (co)homologies
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]

Keywords
ℓ-adic cohomology perverse sheaves decomposition theorem independence of ℓ

Citation

Sun, Shenghao. Independence of $\ell$ for the supports in the decomposition theorem. Duke Math. J. 167 (2018), no. 10, 1803--1823. doi:10.1215/00127094-2017-0059. https://projecteuclid.org/euclid.dmj/1528855662


Export citation

References

  • [1] A. A. Beilinson, J. Bernstein, and P. Deligne, “Faisceaux pervers” in Analysis and Topology on Singular Spaces, I, Astérisque 100, Soc. Math. France, Paris, 1982, 5–171.
  • [2] C. Chevalley, Théorie des groupes de Lie, tome III: Théorèmes généraux sur les algèbres de Lie, Actualités Sci. Ind. 1226, Hermann, Paris, 1955.
  • [3] C. Chin, Independence of $\ell$ in Lafforgue’s theorem, Adv. Math. 180 (2003), 64–86.
  • [4] C. Chin, Independence of $\ell$ of monodromy groups, J. Amer. Math. Soc. 17 (2004), 723–747.
  • [5] P. Deligne, La conjecture de Weil, II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137–252.
  • [6] P. Deligne, Finitude de l’extension de $\mathbb{Q}$ engendrée par des traces de Frobenius, en caractéristique finie, Moscow Math. J. 12 (2012), 497–514.
  • [7] V. Drinfeld, On a conjecture of Deligne, Moscow Math. J. 12 (2012), 515–542.
  • [8] K. Fujiwara, “Independence of $\ell$ for intersection cohomology (after Gabber)” in Algebraic Geometry 2000, Azumino (Hotaka), Adv. Stud. Pure Math. 36, Math. Soc. Japan, Tokyo, 2002, 145–151.
  • [9] L. Illusie, Constructibilité générique et uniformité en $\ell$, preprint, 2010, www.math.u-psud.fr/~illusie.
  • [10] Y. Laszlo and M. Olsson, The six operations for sheaves on Artin stacks, I: Finite coefficients, Publ. Math. Inst. Hautes Études Sci. 107 (2008), 109–168.
  • [11] Y. Laszlo and M. Olsson, Perverse $t$-structure on Artin stacks, Math. Zeit. 261 (2009), 737–748.
  • [12] G. Laumon, Transformation de Fourier, constantes d’équations fonctionnelles et conjecture de Weil, Inst. Hautes Études Sci. Publ. Math. 65 (1987), 131–210.
  • [13] J.-P. Serre, Abelian $l$-Adic Representations and Elliptic Curves, Adv. Book Classics, Addison-Wesley, Redwood City, Calif., 1989.
  • [14] S. Sun, Decomposition theorem for perverse sheaves on Artin stacks over finite fields, Duke Math. J. 161 (2012), 2297–2310.
  • [15] S. Sun, $L$-series of Artin stacks over finite fields, Algebra Number Theory 6 (2012), 47–122.
  • [16] S. Sun and W. Zheng, Parity and symmetry in intersection and ordinary cohomology, Algebra Number Theory 10 (2016), 235–307.
  • [17] W. Zheng, Sur l’indépendance de l en cohomologie l-adique sur les corps locaux, Ann. Sci. Éc. Norm. Supér. (4) 42 (2009), 291–334.
  • [18] W. Zheng, Companions on Artin stacks, preprint, arXiv:1512.08929 [math.AG].