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.