MAGIC037: Local fields

Course details

A core MAGIC course

Semester

Spring 2025
Monday, January 27th to Friday, April 4th

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)

Course forum

Visit the https://v2.maths-magic.ac.uk/forums/magic037-local-fields

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

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Assessment

The assessment for this course will be released on Tuesday 22nd April 2025 at 00:00 and is due in before Monday 5th May 2025 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

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Lectures

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