Mathematics 254---Number Theory

MWF 51 Evans, 12:10--1:00

Arthur Ogus

This will be a basic course in number theory, from a ``modern''geometric point of view. I hope to cover most of the following topics, although not necessarily inthis order: algebraic integer rings, the geometry of numbers, units and the class number, extensions of Dedekind domains,valuations and ramification, different and discriminant, and if possible, zeta and L-functions and the distributions of primes. Our main examples will be quadratic fields and cyclotomic fields. I will assume some knowledge of graduate algebra as background. In particular, students should be comfortable with Galois theory, localization, tensor products, and polynomial rings.

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Differentials and the Different

The Kronecker-Weber Theorem