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)

References >

  • 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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