MAGIC037: Local fields

Course details

A core MAGIC course

Semester

Spring 2026
Monday, January 26th to Friday, April 3rd

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
80

Timetable

Mondays
10:05 - 10:55 (UK)
Fridays
13:05 - 13:55 (UK)

Description

On one hand, local fields form the class of fields which is the next most easiest to study after the class of finite fields, and hence they are quite useful for and applicable in many parts of mathematics, on the other hand, local fields show up in the local study of various parts of mathematics including number theory, algebraic geometry, algebraic topology and areas of mathematical physics. 
 This course will discuss the main examples, features and type of behaviour of local fields and local arithmetic. 


Prerequisites

Some basic knowledge of p-adic numbers will be useful, although we are going to cover them again at the start.

Syllabus

  • p-adic numbers
  • fields with absolute values and valuations
  • polynomials over local fields (Hensel's lemma)
  • extensions of local fields
  • ramification theory
  • ... ? ...

Lecturer

  • Chris Wuthrich

    Chris Wuthrich

    University
    University of Nottingham

Bibliography

No bibliography has been specified for this course.

Assessment

The assessment for this course will be released on Monday 27th April 2026 at 00:00 and is due in before Friday 8th May 2026 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.

Files

Only current consortium members and subscribers have access to these files.

Please log in to view course materials.

Lectures

Please log in to view lecture recordings.