曹锡华代数论坛
报 告 人：Ralf Gerkmann 教授（德国Mainz大学）
报告题目：Rigid cohomology and the computation
of zeta functions over finite fields
报告时间：2009年3月13日（周五）下午1：30-2:30
报告地点：闵行数学楼102报告厅
摘 要
Rigid cohomology as developed by Berthelot provides a theory for varieties over fields of characteristic p whose cohomology spaces are defined over some p-adic field (e.g. the field Q_p of p-adic rationals.) Unlike l-adic (etale) cohomology, the construction of these spaces is quite explicit and accessible for computations. In 2001 Kedlaya suggested to use rigid cohomology in order to compute the zeta function of hyperelliptic curves. Since then his approach has been subject to many generalizations (to more general curves,hypersurfaces, complete intersections) and improvements. The most important one to mention here is a "relative" approach which embeds the variety into an algebraic family and so reduces the computation of the zeta function to the solution of a p-adic differential equation. In my talk I will sketch the main ideas behind all these point counting methods. I will explain how extra structure on the varieties can be used to make the computations more efficient. A relatively new idea is to make use of the singular fibres inside a family. I will comment on the advantage and the open problems related to this approach.
欢迎广大师生参加
数学系2009年3月6日
