Title: Deformation and rigidity of $\ell$-adic sheaves Speaker: 扶磊 (清华大学) Time: 2017-1-11, 17:00-18:00 Place: 110 Abstract: 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. Attachment: Links: 巴黎北京东京算术几何讨论班 On vanishing cycles and duality, after A. Beilinson Filtered de Rham Witt complexes and wildly ramified higher class field theory over finite fields 素数的分布、黎曼假设及随机可乘函数 Local and global geometric structures of perfectoid Shimura varieties Syntomic complexes and p-adic nearby cycles Semisimplicity of geometric monodromy on etale cohomology. Motivic cohomology of formal schemes in characteristic p. The Tamagawa number formula over function fields. On the period conjecture of Gross-Deligne for fibrations Multiple Dirichlet Series, An Historical Survey Colmez' conjecture in average A proof of the local Gan-Gross-Prasad conjecture for unitary groups(III) A proof of the local Gan-Gross-Prasad conjecture for unitary groups(II) A proof of the local Gan-Gross-Prasad conjecture for unitary groups(I) Integrality of p-adic multiple zeta values and application to finite multiple zeta values The BKW method and some applications to quasilinear partial differential equations IV The BKW method and some applications to quasilinear partial differential equations II