中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
数学所讲座
（第85讲）
(The Institute Lecture)
报告人： 扶 磊 教授（清华大学）
题 目：Dwork cohomology, rigid cohomology and exponential sums
时 间：2021.05.12 (星期三), 15:30-17:00(15:00-15:30为茶点时间, 地点: 数学院南楼N920室)
地 点：数学院南楼N204室
摘 要:
A conjecture of Weil says that the ζ-function of an algebraic variety over a finite field is rational. The first proof of this conjecture was given by Dwork. He expressed the ζ-function in terms of the traces of a completely continuous operator on a complex of some p-adic Banach spaces. The complex has finite dimensional cohomology groups. This gives the rationality of the ζ-function. We explain Dwork’s method, its relation with Betherlot’s rigid cohomology theory, and how to extend this method to study family of exponential sums.
数学所讲座(The Institute Lecture)：
旨在讲解现代数学的重要内容及其思想、方法和影响，扩展我们科研人员和研究生的视野、提高数学修养和加强相互交流、增强学术气氛。时间定在每月（寒暑假另外安排）的第一个星期三。
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