报告人：扶 磊 (清华大学)
题 目：Deformation and rigidity of $\ell$-adic sheaves
时 间：2017.01.11（星期三），17:00-18:00
地 点：晨兴110室
摘 要：Let $X$ be a smooth connected algebraic curve over an algebraically closed field, let $S$ be a finite closed subset in $X$, and let $\mathcal F_0$ be a lisse $\ell$-torsion sheaf on $X-S$. We study the deformation of $\mathcal F_0$. 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 $\overline{\mathbb Q}_\ell$-sheaf $\mathcal F$ is irreducible and physically rigid, then it is cohomologically rigid in the sense that $\chi(X,j_\ast\mathcal End(\mathcal F))=2$, where $j:X-S\to X$ is the open immersion.
