Jerusalem Mathematics Colloquium

Thursday, 6 November 1997, 4:00 pm
Mathematics Bldg., lecture hall 2

Dr. Amnon Besser (University of Durham, UK)

"p-adic integration and its applications"

Abstract: This lecture is intended as an introduction to the integration theory of Coleman, its generalisation and applications in arithmetic algebraic geometry. In the first part of the lecture I will introduce some of the problems I am interested in. To give an example I will mostly talk about the problem of describing the group of rational points on elliptic curves: solutions in rational numbers x and y to the cubic equation y^2=x^3+ax+b for some rational numbers a and b . I will say something about the techniques from complex analysis used and sketch the generalisation to higher dimensions. In the second part of the talk I will introduce the basics of p-adic analysis that can be used to treat the same problems and in particular the Coleman integral. I will try to stress the similarities and the differences between the p-adics and the complex numbers. I will explain the basic idea behind the Coleman integral using the motivating example of the p-adic logarithm. In the last part of the lecture I will talk about my own work, generalising the Coleman integral to higher dimensions.

List of talks, fall 1997