Model Theory and Algebra of Valued Fields
This is a graduate lecture course given jointly by Jochen Koenigsmann (Oxford) and Deirdre Haskell (McMaster). The schedule is roughly as follows:
|Week 1||Basics on valuations and places|
|Week 2||Extensions and Henselian valued fields|
|Week 3||Model theory of valued fields, especially quantifier elimination results|
|Week 4||Topological aspects|
|Week 5||First-order definability of Henselian valued rings|
|Week 6||Local-global principles, regularly closed fields|
|Week 7||Galois theory of valued fields|
|Week 8||Quick look at Hilbert's tenth problem, anabelian geometry and/or the inverse Galois problem|
Lectures are timetabled as follows:
Weeks 1-2, 4-8, to be given by Jochen Koenigsmann on Wednesdays and Fridays at 10am in SR1. The algebraic aspects of the theory will be covered in these lectures. Week 3, to be given by Deirdre Haskell in 6 hours: Wednesday 10-12, Thursday 11-1, Friday 9 -11. These lectures will cover the model-theoretic aspects of the theory.
Lecture notes for the course will be posted and periodically updated (with inevitable corrections).