|Faculty of Science|
Department of Mathematics
|MATH 600 / D|
Topics in Algebraic K-theory
|Class schedule:||Tue Thu<br\>11:00 am - 12:30 pm|
|Office hours:||Wed 11:00 am - 1:00 pm|
or by appointment
|No pages found.|
Algebraic K-Theory originated in the 1960's and has today grown into a vast, active branch of mathematics. It has made inroads into other areas of mathematics like Algebraic topology, Algebraic geometry and Algebraic Number Theory . After a brief introduction to the K-groups, we shall largely focus on the groups , and . The preliminaries will constitute a third of the course. We will provide various snapshots of the linkages of K-theory to some of the areas mentioned above. We shall then study the groups for a field of characteristic not 2, and its connections with the algebraic theory of quadratic forms over the field , and to the Galois cohomology groups , leading to the statement of the Milnor conjectures, now a theorem due to Voevodsky. There will be no final exam for this course. I will try to make the course as self-contained as possible, pointing to further readings as the course progresses. There will be periodic assignments which will serve as a basis for assigning a final grade.
- Homework 1 ( Due date: Sep 27, 2011 )corrections
- Homework 2 ( Due date: Oct 11, 2011 )corrections
- Homework 3 ( Due Date: Oct 25, 2011 )
- Homework 4 ( Due Date: Nov 15, 2011 )
- Homework 5 (Due Date: Nov 29, 2011)
- Atiyah, Michael F, and D W. Anderson. K-theory. New York: W.A. Benjamin, 1967.
- Bass, Hyman. 1968. Algebraic K-theory. New York: W.A. Benjamin.
- Bass, Hyman, and Amit Roy. 1967. Lectures on topics in algebraic k-theory. Bombay: Tata Institute of Fundamental Research.
- Milnor, John W. Introduction to Algebraic K-Theory. Princeton, N.J: Princeton University Press, 1971.
- Rosenberg, J. Algebraic K-Theory and Its Applications. New York: Springer-Verlag, 1994.
- Srinivas, V. Algebraic K-Theory. Boston: Birkhäuser, 2008
- Weibel, Charles. The K-book: An introduction to algebraic K-theory (a graduate textbook in progress)..
- Notes on Steinberg relations
- Notes on Profinite Galois cohomology
Jerome will lecture on Nov 8 and Shane on Nov 22. There will be no lectures on Nov 10 and Nov 17. There *will* be lecture by me on Nov 15.
SUGGESTED ADDITIONAL READING
Bass, H.; Tate, J. The Milnor ring of a global field. Algebraic K-theory, II: "Classical algebraic K-theory and connections with arithmetic (Proc. Conf., Seattle, Wash., Battelle Memorial Inst., 1972), pp. 349–446. Lecture Notes in Math., Vol. 342, Springer, Berlin, 1973.
Milnor, John Algebraic K-theory and quadratic forms. Invent. Math. 9 1969/1970 318–344.