Field Arithmetic

UGA MATH 8430, Spring 2017.
Field extensions, Galois theory and inverse Galois theory, field invariants, Galois cohomology, and open problems.

Lecture 1: Philosophy and basic notions
Lecture 2: Finite field extensions
Lecture 3: Algebraic closures
Lecture 4: Galois extensions
Lecture 5: Transcendence bases, and Pell's equation I
Lecture 6: Extensions and the revenge of Pell's equation
Lecture 7: Profinite Galois theory
Lecture 8: Galois Cohomology
Lecture 9: The idea of the Brauer-Manin obstruction
Lecture 10: Brauer-Manin obstructions, part 2: the structure of the Brauer group
Lecture 11: Brauer-Manin obstructions, part 3: computing the Brauer group of varieties