250063 VO p-adic analysis and number theory (2013W)

The aim of the course is to give an introduction to p-adic analysis and its connections with and applications to number theory. The first such application occured in local class field theory with the explicit computation of the local reciprocity law und in the computation of the zeta function of a projective variety. In recent years this has developed into a p-adic analogon of diophantine geometry in particular with respect to p-adic analoga of cohomology theories. In the course we want to explain the origins and basic ideas of the theory by looking at the simplest example of cyclotomic fields. We will agree on prerequisites and the precise contents of the course in a first meeting on Thirsday 3.10. It would be ideal if participants had a basic knowledge of algebraic number theory in particular of local fields.