Lecturer: Dr. Andrey Soldatenkov
Exams:
First date: Friday 24.07.20, 9:00 - 17:00
Second date: Friday 09.10.20, 9:00 - 17:00
The exams will be in the form of "Take Home Klausur": problems will be published in the morning on the Moodle page of the course and participants will have time until the evening to submit their solutions via Moodle or by e-mail (scans or readable photos of handwritten solutions will be acceptable; you do not need to typeset your solutions in LaTeX). Please register for the exam in AGNES.
Lectures: Monday 09:00 - 11:00, 11:00 - 13:00,
Online lectures in Zoom will start on 20.04.20. To get access to the online lectures you need to enrol on the Moodle course. The enrolment key will be sent out by e-mail to all students registered for the course in AGNES. You will find a link to the Zoom meetings on the right hand side of the Moodle page of the course. You can contact me by e-mail in case of any problems.
Exercise sessions (by Jan Hesmert, e-mail: jan.hesmert at hu-berlin.de): Wednesday 11:00 - 13:00
The exercise sessions will also take place in Zoom starting on 22.04.20
We will give an introduction to the methods of algebraic number theory. Among the topics to be discussed: number fields and their rings of integers, Dedekind rings, ideal classes and the unit theorem, valuations and completions, field extensions and ramification.
Prerequisites. Standard undergraduate algebra (basic properties of the ring of integers and its quotient rings; groups; polynomial rings; finitely generated abelian groups). We will also assume familiarity with Galois theory, but all necessary facts will be recalled (mostly without proofs).
A. Fröhlich, M. J. Taylor, Algebraic number theory, Cambridge University Press, 1991
K. Ireland, M. Rosen, A classical introduction to modern number theory, Springer, 1990
J. Neukirch, Algebraische Zahlentheorie, Springer, 1992
P. Samuel, Algebraic theory of numbers, Houghton Mifflin Co., 1970
H. P. F. Swinnerton-Dyer, A brief guide to algebraic number theory, Cambridge University Press, 2001
R. B. Ash, online notes on algebraic number theory
B. Conrad, online notes on algebraic number theory
M. F. Atiyah, I. G. Macdonald, Introduction to commutative algebra. Addison-Wesley, 1969
J. S. Milne, Fields and Galois Theory, online
J. W. S. Cassels, A. Fröhlich, Algebraic number theory, Academic Press, 1986
S. Lang, Algebraic number theory, Springer, 1994
J. S. Milne, various course notes
J.-P. Serre, Local fields, Springer, 1979