Math 612 Arithmetic and Geometry of Linear Algebraic Groups
Semester: Spring 2015


Graduate Course

Inst : 
Asher Auel
asher * auel AT yale
* edu 
Time : 
Tue Thu 2:30  3:45 am 
Loct : 
LOM 205 

Office : 
LOM 210 
Phone : 
(203) 4324187 
Office hours : 
Wed 2:00  3:00 pm 

Take the final exam.

Detailed course syllabus.

Description of course:
This course approaches the subject of linear algebraic groups from the
perspective of applications to number theory and algebraic
geometry. Specific instances could include the HasseMinkowski theorem and
the classification of classical groups over number fields; and the
theorems of Tsen and Lang on the cohomological properties of function
fields with applications to families of projective homogeneous
spaces. Following the approach of Serre, we highlight the theory of
cohomological invariants for related algebraic structures, such as
quadratic, symplectic, and hermitian forms, central simple algebras,
octonion algebras, and Jordan algebras. The requisite background on
algebraic geometry and Galois cohomology is introduced throughout the course.
Expected background:
Familiarity with algebra and basic Galois theory. Some
previous experience with basic algebraic geometry, representation
theory, or algebraic number theory is helpful, but not essential.
Grading:
Your grade will be based on the takehome final exam.
