Instructor: W. Banks

Description: We will follow Andre Weil's classic text. This is an exposition of algebraic number theory and class field theory, handling in a unified manner all local and global fields, the latter being finite algebraic extensions over the rational numbers or over a field of rational functions of one variable with a strictly finite field of constants. We will study the construction, classification, and structural properties of such fields and many other related topics.

Text: A. Weil, "Basic number theory" (3rd edition).
Die Grundlehren der Mathematischen Wissenschaften, Band 144.
Springer-Verlag, New York-Berlin, 1974.

Prerequisites: Math 8410 or 8210 required, in addition Math 8250 recommended.