MAT9570: Algebraic K-theory
Link to the official course page
Information about teaching, examination, etc.
Rough plan for the lectures
- Category theory [Mac Lane]
- Categories and functors
- Discrete and additive representations
- (De-)categorification
- Limits and colimits
- Adjoint pairs
- (ETC)
- Weak equivalences and quasi-fibrations
- Simplicial sets and spaces
- The gluing lemma
- The realization lemma
- A fibration criterion
- The nerve of a category
- Quillen's Theorem A
- Quillen's Theorem B
- Categories with cofibrations and weak equivalences
- The S.-construction
- K-theory of finite sets
- The additivity theorem
- The approximation theorem
- The fibration theorem
- Exact categories
- Segal subdivision
- The Q-construction
- Dévissage
- Localization
Some foundational papers
- Daniel Quillen, Higher algebraic K-theory. I, Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), pp. 85--147. Lecture Notes in Math., Vol. 341, Springer, Berlin 1973.
- Graeme Segal, Categories and cohomology theories, Topology 13 (1974), 293--312.
- Friedhelm Waldhausen, Algebraic K-theory of spaces, Algebraic and geometric topology (New Brunswick, N.J., 1983), 318--419, Lecture Notes in Math., 1126, Springer, Berlin, 1985.
- Bob Thomason and Thomas Trobaugh, Higher algebraic K-theory of schemes and of derived categories, The Grothendieck Festschrift, Vol. III, 247--435, Progr. Math., 88, Birkhäuser Boston, Boston, MA, 1990.
Some books on algebraic K-theory
- Jon Berrick, An approach to algebraic K-theory, Research Notes in Mathematics, 56, Pitman (Advanced Publishing Program), Boston, Mass.--London, 1982.
- Eric Friedlander and Dan Grayson (editors), Handbook of K-theory. Vol. 1, 2, Springer-Verlag, Berlin, 2005.
- Dan Grayson, Algebraic K-theory, http://www.math.uiuc.edu/~dan/Courses/2003/Spring/416/GraysonKtheory.pdf
- John Milnor, Introduction to algebraic K-theory, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, NJ, 1971.
- Jonathan Rosenberg, Algebraic K-theory and its applications, Graduate Texts in Mathematics, 147, Springer-Verlag, New York, 1994.
- Vasudevan Srinivas, Algebraic K-theory, Second edition. Progress in Mathematics, 90, Birkhäuser Boston, Inc., Boston, MA, 1996.
- Chuck Weibel, The K-book: An introduction to algebraic K-theory, http://www.math.rutgers.edu/~weibel/Kbook.html