Morningside Center of Mathematics
Chinese Academy of Sciences
Morningside Center of Mathematics
Chinese Academy of Sciences
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. |
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