Laboratoire Alexander Grothendieck, Institut des Hautes Études Scientifiques,
Morningside Center of Mathematics, Chinese Academy of Sciences,
Département des Sciences Mathématiques de l'Université de Tokyo

Ahmed Abbes (CNRS, IHÉS), Fabrice Orgogozo (CNRS, École polytechnique), Takeshi Saito (Université de Tokyo),
Atsushi Shiho (Université de Tokyo), Ye Tian (Morningside Center for Mathematics),
Takeshi Tsuji (Université de Tokyo), Weizhe Zheng (Morningside Center for Mathematics)

Mercredi 11 janvier 2017 de 10h à 11h

Lei Fu (Tsinghua University)

Deformation and rigidity of l-adic sheaves

Let X be a smooth connected algebraic curve over an algebraically closed field, let S be a finite closed subset in X, and let F_0 be a lisse l-torsion sheaf on X-S. We study the deformation of F_0. The universal deformation space is a formal scheme. Its generic fiber has a rigid analytic space structure. By studying this rigid analytic space, we prove a conjecture of Katz which says that if a lisse $\overline{Q}_\ell$-sheaf F is irreducible and physically rigid, then it is cohomologically rigid in the sense that \chi(X,j_*End(F))=2, where j:X-S--> X is the open immersion.