MAT9570: Algebraic Ktheory
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)
 Homotopy theory [Hatcher, GoerssJardine, Waldhausen]
 Weak equivalences and quasifibrations
 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 Ktheory [Waldhausen, R.]
 Categories with cofibrations and weak equivalences
 The S.construction
 Ktheory of finite sets
 The additivity theorem
 The approximation theorem
 The fibration theorem
 Quillen Ktheory [Quillen]
 Exact categories
 Segal subdivision
 The Qconstruction
 Dévissage
 Localization
Some foundational papers

Daniel Quillen,
Higher algebraic Ktheory. I,
Algebraic Ktheory, I: Higher Ktheories (Proc. Conf., Battelle
Memorial Inst., Seattle, Wash., 1972), pp. 85147. Lecture Notes in
Math., Vol. 341, Springer, Berlin 1973.

Graeme Segal,
Categories and cohomology theories,
Topology 13 (1974), 293312.

Friedhelm Waldhausen,
Algebraic Ktheory of spaces,
Algebraic and geometric topology (New Brunswick, N.J., 1983), 318419,
Lecture Notes in Math., 1126, Springer, Berlin, 1985.

Bob Thomason and Thomas Trobaugh,
Higher algebraic Ktheory of schemes and of derived categories,
The Grothendieck Festschrift, Vol. III, 247435, Progr. Math., 88,
Birkhäuser Boston, Boston, MA, 1990.
Some books on algebraic Ktheory

Jon Berrick,
An approach to algebraic Ktheory,
Research Notes in Mathematics, 56,
Pitman (Advanced Publishing Program), Boston, Mass.London, 1982.

Eric Friedlander and Dan Grayson (editors),
Handbook of Ktheory. Vol. 1, 2,
SpringerVerlag, Berlin, 2005.

Dan Grayson,
Algebraic Ktheory,
http://www.math.uiuc.edu/~dan/Courses/2003/Spring/416/GraysonKtheory.pdf

John Milnor,
Introduction to algebraic Ktheory,
Annals of Mathematics Studies, No. 72,
Princeton University Press, Princeton, NJ, 1971.

Jonathan Rosenberg,
Algebraic Ktheory and its applications,
Graduate Texts in Mathematics, 147,
SpringerVerlag, New York, 1994.

Vasudevan Srinivas,
Algebraic Ktheory,
Second edition. Progress in Mathematics, 90,
Birkhäuser Boston, Inc., Boston, MA, 1996.

Chuck Weibel,
The Kbook: An introduction to algebraic Ktheory,
http://www.math.rutgers.edu/~weibel/Kbook.html
John Rognes / December 16th 2009