Topics in Number Theory (WI21)
Introduction to Linear Algebraic Groups
- Lectures: Monday, Wednesday, Friday, block F (2:35 - 3:40 p.m. EST)
- Course type: Remote with synchronous components (RSC)
- x-period: Thursday, block FX (1:40 - 2:30 p.m. EST)
- Dates: 7 January 2021 - 10 March 2021
- Zoom Link: Use navigation bar. Send me an email if you have any problems.
- Instructor: John Voight
- E-mail: email@example.com
- Office hours: during x-hour, or please make an appointment by email!
- Course Web Page: https://canvas.dartmouth.edu/courses/44283 (or http://www.math.dartmouth.edu/~m105w21/ redirects)
- Prerequisites: Math 101 or equivalent, but a healthy mathematical appetite is sufficient. The course is designed to have multiple entry points, depending on your background.
- James E. Humphreys, Linear Algebraic Groups, 1981.
- W.C. Waterhouse, Introduction to Affine Group Schemes, 1979.
- Gunter Malle and Donna Testerman, Linear Algebraic Groups and Finite Groups of Lie Type, 2011.
- T.A. Springer, Linear Algebraic Groups, 2nd ed., 1998.
- Willem Adriaan de Graaf, Computation with Linear Algebraic Groups, 2017.
- Grading: Grade will be based on knuggets (see Grading).
A linear algebraic group is a subgroup of invertible matrices defined by polynomial equations (in the matrix entries and the inverse of the determinant). Linear algebraic groups underpin all of mathematics, and in this course we will study them from an abstract perspective. Our point of view: seek out all of the fun of linear algebra and group theory, but from the point of view of algebraic geometry. In particular, we will seek out the remarkable classification of the reductive groups, the most important linear algebraic groups in practice.
By the end of this course, you should be able to understand of the basic structures of linear algebraic groups: define terms, explain their significance, and apply them in context.
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