Research seminar on Algebraic K-Theory
The topic of the seminar for this semester is (higher) algebraic K
-theory. The plan is to study first some classical papers on the subject (Grayson, Quillen, Waldhausen,...)
and then move towards a more modern approach.
Time and place:
Fridays 15:30-17:00 Huygensgebouw room HG03.085 (Hilbert's room).
Note that Talks 07, 08 and 09 will be on Monday in room HG01.028 from 15:00.
Schedule for the talks >
Talk 01, 03/10/14:
The Q-construction (Matan Prasma)
Talk 02, 10/10/14:
On Quillen's Theorem A and B (Javier J. Gutiérrez)
Talk 03, 17/10/14:
The localization theorem for abelian categories (Joost Nuiten)
- Talk 04, 24/10/14:
The S-1S construction (Ieke Moerdijk)
- Talk 05, 31/10/14:
The Waldhausen's S-construction (I) (Giovanni Caviglia)
- There will be
no session on 07/11/14 due to the GQT colloquium in Zandvoort.
- Talk 06, 14/11/14:
The Waldhausen's S-construction (II) (Javier J. Gutiérrez)
- Talk 07, 24/11/14:
The Waldhausen's S-construction (III) (Giovanni Caviglia)
- Talk 08, 24/11/14:
On the relation between the Q-construction and the S-construction (Joost Nuiten)
- Talk 09, 01/12/14:
On Quillen's plus construction (Matan Prasma)
- Talk 10, 12/12/14:
On the group completion (Ieke Moerdijk)
- H. Bass, Algebraic K-theory. W. A. Benjamin, Inc., New York-Amsterdam, 1968.
- A. Blumberg and M. Mandell, Algebraic K-theory and abstract homotopy theory.
Adv. Math. 226 (2011), no. 4, 3760-3812.
- A. Elmendorf and M. Mandell, Ring, modules and algebras in infinite loop space theory.
Adv. Math 205 (2006), 163-228.
- H. Gillet and D. R. Grayson, The loop space of the Q-construction.
Illinois J. Math. 31 (1987), 574-597. (+erratum)
- D. R. Grayson, Higher algebraic K-theory II.
Algebraic K-theory, Evanston 1976, Lecture Notes in Math. 551, Springer,1976.
- D. Quillen, Higher algebraic K-theory I.
Higher K-theories, Battelle 1972, Lecture Notes in Math. 341, Springer, 1973 .
- D. Quillen, Higher algebraic K-theory.
Proceedings of the ICM, Vancouver 1974, Canad. Math. Congress, 1973.
- D. Quillen, Higher K-theory for categories with exact sequences.
Proc. Sympos. Algebraic Topology, Oxford 1972, London Math. Soc. Lecture Note Ser. 11, 1974.
- F. Waldhausen, Algebraic K-theory of spaces.
Algebraic and geometric topology, New Brunswick, 1983, Lecture Notes
in Math., 1126, Springer, 1985.
- F. Waldhausen, Algebraic K-theory of spaces, localization,
and the chromatic filtration of stable homotopy.
Algebraic topology, Aarhus 1982, Lecture Notes in Math. 1051,Springer, 1984.
- F. Waldhausen, Operations in the algebraic K-theory of spaces.
Algebraic K-theory, Part II, Oberwolfach 1980), Lecture Notes in Math. 967, Springer, 1982.
- C. Weibel, The K-book: an introduction to algebraic K-theory. Graduate Studies in Math. vol. 145, AMS, 2013.
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