Math 608 Introduction to Arithmetic Geometry Semester: Spring 2016

Description of course: This course will explore some of the major themes in arithmetic geometry, i.e., the study of algebraic varieties over arbitrary fields. Topics will include quadratic forms and the Brauer group, Galois cohomology and descent, principal homogeneous spaces and local-global principles, as well as the existence of rational points and rational parametrizations. Of particular interest will be varieties over finite fields, valued fields, real closed fields, C_i-fields, number fields, and functions fields. Recurring objects of study throughout the course will be quadric hypersurfaces and rational surfaces from an arithmetic and geometry point of view.

Expected background: Some prior experience with algebra, Galois theory, and algebraic geometry will be very helpful but not strictly necessary. Can be taken in conjunction with a beginning algebraic geometry course.

Grading: Your grade will be based on class participation and a final project.