Model Theory for Algebra and Algebraic Geometry
Spring 2010
Universite Paris-Sud Orsay
Course Meeting:
- Mon May 17, Wed May 19
- Wed May 26, Thu May 27
- Mon May 31, Wed June 2, Thu June 3
- Thu June 10
Monday and Wednesday lectures are at 10:00-12:00 in salle 113-115
Thursday lectures are 14:15-16:15 in salle 225-227.
Instructor: David Marker
e-mail: marker@math.uic.edu
course webpage:
http://www.math.uic.edu/~marker/orsay
Description
These lectures will be an introduction to some basic connections to algebra and algebraic
geometry. The basic topics covered will include:
- Logic, Language and Structures
- The Compactness Theorem and applications
- Ultraproducts and a proof of compactness
- Ax's Theorem that injective polynomial maps are surjective
- Quantifer elimination tests
- the model theory of algebraically closed fields and algebraic geometry
- the model theory of real closed fields and semialgebraic geometry
I also intend to discuss some advanced topics including:
- o-minimality, subanalytic geometry and exponentiation
- Asymptotic bounds on the number of rational points on o-minimal sets
and Diophantine applications
Texts
- D. Marker, Model Theory: An Introduction, Graduate Texts in Mathematics 217,
Springer, New York, 2002.
Lecture Notes
I will try to provide lecture notes for some of my lectures. The notes will contain some material that will
not be covered in the lectures.
Exercises