Course Description and Grading BreakdownThe course will give an introduction to algebraic K-theory. We start with the basics on K_0,K_1,K_2 and Quillen’s definition and fundamental theorems about higher algebraic K-theory. Then we’ll discuss in some details the algebraic K-theory of number rings, in particular finite generation. At the end I’ll hope to discuss some more recent developments , notably the work of Tabuada et al. on a characterization of higher algebraic K-theory by a universal property. Prerequisites are some background in algebraic geometry (Ma130), algebraic number theory (Ma160) and algebraic topology (Ma151). While one can probably follow with a minimal background in the first two subjects, we will rely on algebraic topology more seriously. In particular, some knowledge about category theory, H-spaces and the description of homotopy types by simplicial sets will be necessary. However, I might also develop some of the background material in class. Course Meeting Time and LocationTuesday and Thursday 1:00 - 2:25 pm 289 Linde Course Instructor Contact Information and Office Hours264 Linde Hall Course Schedule and Textbook
Course PoliciesPassing the class is dependent on giving a successful presentation at the end. Assignments
Midterm and Final ExamCollaboration Table
* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them. |