## Admission requirements

A thorough mastery of the material in the course Algebraic Number Theory (offered through Mastermath) is required.

## Description

This course is a sequel to the Algebraic Number Theory course, and treats the basic theory of local fields. This will include both algebraic material (valuations, extensions, ramification theory, Kronecker-Weber, etc) and analytic material (p-adic analytic functions, Mahler’s theorem, p-adic L-functions, etc).

## Course objectives

At the end of this course, the student will be familiar with the local theory of number fields, and master algebraic as well as analytic techniques that provide, besides some immediate applications, an introduction to some contemporary research themes in number theory.

## Mode of instruction

weekly lectures, homework, and exercise classes

## Assessment method

The final grade consists of homework (20%, no retake) and an oral (retake) exam (80%).

## Literature

Course notes and relevant resources will be distributed to students.

## Contact

Peter Stevenhagen (psh[at]math.leidenuniv.nl)

Jan Vonk (j.b.vonk[at]math.leidenuniv.nl)