# 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 ${\displaystyle K_{0}~}$, ${\displaystyle K_{1}~}$ and ${\displaystyle K_{2}~}$. 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 ${\displaystyle K_{i}(F)~}$ for a field ${\displaystyle F~}$ of characteristic not 2, and its connections with the algebraic theory of quadratic forms over the field ${\displaystyle F~}$, and to the Galois cohomology groups ${\displaystyle H_{{\acute {e}}t}^{i}(F,\mathbb {Z} /2\mathbb {Z} )~}$, 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.

## 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