Lectures: 11:00-12:00, Tuesdays, Thursdays and Saturdays
Replacement lecture: Tuesday 11 March, 1:00-2:00, MR5 (I'll give people time to grab a snadwich before starting.)
First examples class: Wednesday 19 February, 2:00-3:30, MR3
Example sheet #1 (corrected) - Solutions
Second examples class: Wednesday 5 March, 2:00-3:30, MR3
Third examples class: (Thursday 24 April, 11:00-1:00)
Optional Easter term lectures on class field theory: handwritten notes
Course description (from the Part III handbook):
In recent years one of the most growing areas of research in number theory has been Arithmetic Algebraic Geometry, in which the techniques of algebraic number theory and abstract algebraic geometry are applied to solve a wide range of deep number-theoretic problems. These include the celebrated proof of Fermat's Last Theorem, the Birch-Swinnerton-Dyer conjectures, the Langlands Programme and the study of special values of L-functions. In this course we will study one half of the picture: Algebraic Number Theory. I will assume some familiarity with the basic ideas of number fields, although these will be reviewed briefly at the beginning of the course. (The relevant algebra will also be found in the Commutative Algebra course.)
Topics likely to be covered (not in order):
Prerequisite Mathematics
A first course in number fields (or equivalent reading). Basic algebra up to and including Galois theory is essential.
Literature
a.j.scholl@dpmms.cam.ac.uk