Course:MATH600D
Faculty of Science Department of Mathematics 


MATH 600 / D Topics in Algebraic Ktheory 

Instructor:  Sujatha Ramdorai 
Office:  MATX 1201 
Class schedule:  Tue Thu 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 KTheory 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 Kgroups, 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 Ktheory 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 selfcontained 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. Ktheory. New York: W.A. Benjamin, 1967.
 Bass, Hyman. 1968. Algebraic Ktheory. New York: W.A. Benjamin.
 Bass, Hyman, and Amit Roy. 1967. Lectures on topics in algebraic ktheory. Bombay: Tata Institute of Fundamental Research.
 Milnor, John W. Introduction to Algebraic KTheory. Princeton, N.J: Princeton University Press, 1971.
 Rosenberg, J. Algebraic KTheory and Its Applications. New York: SpringerVerlag, 1994.
 Srinivas, V. Algebraic KTheory. Boston: Birkhäuser, 2008
 Weibel, Charles. The Kbook: An introduction to algebraic Ktheory (a graduate textbook in progress)..
 Notes on Steinberg relations
 Notes on Profinite Galois cohomology
External links
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 Ktheory, II: "Classical algebraic Ktheory 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 Ktheory and quadratic forms. Invent. Math. 9 1969/1970 318–344.