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"
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