Algebraic K-Theory

Course Description and Grading Breakdown

The 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 Location
Tuesday and Thursday
1:00 - 2:25 pm
289 Linde

Course Instructor Contact Information and Office Hours
264 Linde Hall

Course Schedule and Textbook

 DateTopic 
  
  


Course Policies

Passing the class is dependent on giving a successful presentation at the end.


Assignments
 Date PostedAssignment Due Date 
   
   


Midterm and Final Exam


Collaboration Table
 HomeworkExams
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
InternetYESNO
Your notes (taken in class)YESYES
Class notes of othersYESNO
Your hand copies of class notes of othersYESYES
Photocopies of class notes of othersYESNO
Electronic copies of class notes of othersYESNO
Course handoutsYESYES
Your returned homework / examsYESYES
Solutions to homework / exams (posted on webpage)YESYES
Homework / exams of previous yearsNONO
Solutions to homework / exams of previous yearsNONO
Emails from TAsYESNO
You may:

Discuss problems with othersYESNO
Look at communal materials while writing up solutionsYESNO
Look at individual written work of othersNONO
Post about problems onlineNONO
For computational aids, you may use:

CalculatorsYES*NO
ComputersYES*NO

* 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.