Math 129: Algebraic Number Theory Homework Assignment 11 (last assignment)

William Stein

Due: Thursday, May 6, 2004 (last day of class!)

1. Turn in a very rough draft or outline of your project. Turn anything in and get a perfect score on this homework problem.

2. Prove that the product formula holds for F(t) similar to the proof we gave in class using Ostrowski’s theorem for Q. You may use the analogue of Ostrowski’s theorem for F(t), which you had on a previous homework assignment. (Don’t give a measure-theoretic proof.)

3. Prove Theorem 14.5 from the lecture, that “The global field K is discrete in 𝔸_{K} and the quotient 𝔸_{K}^{+}/K^{+} of additive groups is compact in the quotient topology.” in the case when K is a finite extension of F(t), where F is a finite field.