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
- Limits and colimits
- Adjoint pairs
- Homotopy theory [Hatcher, Goerss-Jardine, Waldhausen]
- Weak equivalences and quasi-fibrations
- Simplicial sets and spaces
- The gluing lemma
- The realization lemma
- A fibration criterion
- Classifying spaces [Quillen]
- The nerve of a category
- Quillen's Theorem A
- Quillen's Theorem B
- Waldhausen K-theory [Waldhausen, R.]
- Categories with cofibrations and weak equivalences
- The S.-construction
- K-theory of finite sets
- The additivity theorem
- The approximation theorem
- The fibration theorem
- Quillen K-theory [Quillen]
- Exact categories
- Segal subdivision
- The Q-construction
Some foundational papers
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.
Categories and cohomology theories,
Topology 13 (1974), 293--312.
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
John Rognes / December 16th 2009
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.
Introduction to algebraic K-theory,
Annals of Mathematics Studies, No. 72,
Princeton University Press, Princeton, NJ, 1971.
Algebraic K-theory and its applications,
Graduate Texts in Mathematics, 147,
Springer-Verlag, New York, 1994.
Second edition. Progress in Mathematics, 90,
Birkhäuser Boston, Inc., Boston, MA, 1996.
The K-book: An introduction to algebraic K-theory,