Course:MATH600D

Faculty of Science Department of Mathematics
MATH 600 / D Topics in Algebraic K-theory
Instructor:	Sujatha Ramdorai
	email
Office:	MATX 1201
Class schedule:	Tue Thu<br\>11:00 am - 12:30 pm
Classroom:	MATX 1102
Office hours:	Wed 11:00 am - 1:00 pm or by appointment
Course pages
	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 $K_{0}~$, $K_{1}~$ and $K_{2}~$. 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 $K_{i}(F)~$ for a field $F~$ of characteristic not 2, and its connections with the algebraic theory of quadratic forms over the field $F~$, and to the Galois cohomology groups $H_{{\acute {e}}t}^{i}(F,\mathbb {Z} /2\mathbb {Z} )~$, 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.

Homeworks

• 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)

References

• 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

External links

• K-theory Preprint Archives
• Mario Garcia Armas's Math 600D webpage
• Brauer groups

Announcements

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.