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Workgroup on Number Theory and Algebraic Geometry

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 1.027

Address
Englerstraße 2, 76131 Karlsruhe

Office hours:
Mo - Fr, 9.15 - 11.45

Tel.: +49 721 608 43041

Fax.: +49 721 608 44244

Algebra (englisch) (Winter Semester 2014/15)

Lecturer: Prof. Dr. Frank Herrlich
Classes: Lecture (0102200), Problem class (0102300)
Weekly hours: 4+2


The course will give an introduction to basic concepts in field threory and ring theory.
The lectures will be in English.

In the first week, the lecture takes place on Wednesday and Thursday (9.45 to 11.15). The first problem class is on Friday, October 24, from 11.30 to 13.00.

In the week before Christmas the lecture and the tutorial will be swapped. The lecture will take place on Tuesday, 16.12.2014, 17:30 in the room 1C-03 (Allianzgebäude) and the tutorial will take place on Wednesday, 17.12.2014, 9:45 in the lecture hall AOC 201 (chemistry building).

There will be no tutorial at 23 December 2014.

Schedule
Lecture: Wednesday 9:45-11:15 AOC 201 Begin: 22.10.2014, End: 13.2.2015
Friday 11:30-13:00 Neuer Hörsaal
Problem class: Thursday 9:45-11:15 Chemie-Hörsaal II Begin: 24.10.2014
Lecturers
Lecturer Prof. Dr. Frank Herrlich
Office hours: Fr, 14.00 - 15.00 Uhr
Room 1.029 Kollegiengebäude Mathematik (20.30)
Email: herrlich@kit.edu
Problem classes Sven Caspart
Office hours: (nearly) always when I'm in the office
Room 1.025 Kollegiengebäude Mathematik (20.30)
Email: sven.caspart@kit.edu

Contents
1. Field theory
Algebraic field extensions, separability, normal extensions, Galois theory.
Roots of unity, cyclotomic fields, solution of polynomial equations by radicals, solvable groups.
2. Valuation theory
Valuations, absolute values and norms on rings.
p-adic numbers, nonarchimedean valuations.
Discrete valuation rings, extension of valuations.
3. Ring theory
Modules over rings, tensor product of modules, multilinear algebra.
Noetherian rings, ring of polynomials, Hilbert's basis theorem.
Integral ring extensions, integral closure; normalization, Dedekind domains.

Exercise Sheets

The exercise sheets can be found in the Ilias course.

Examination

The oral exams will take place on 2 March, 16 March and 30 March 2015. Students who want to take the exam should sign in to the time table which can be found in the secretary's office (room 4A-21.1, Allianz building). Possible times are listed in the table there.
In addition you must register the exam in the Campus Management for Students.