Transfer maps and projection formulas

Preprint English OPEN
Tabuada, Goncalo (2010)
  • Subject: Mathematics - Algebraic Topology | 18D20, 19D55, 14F05 | Mathematics - Algebraic Geometry | Mathematics - K-Theory and Homology
    arxiv: Mathematics::K-Theory and Homology

Transfer maps and projection formulas are undoubtedly one of the key tools in the development and computation of (co)homology theories. In this note we develop an unified treatment of transfer maps and projection formulas in the non-commutative setting of dg categories. As an application, we obtain transfer maps and projection formulas in algebraic K-theory, cyclic homology, topological cyclic homology, and other scheme invariants.
  • References (23)
    23 references, page 1 of 3

    [1] A. Blumberg and M. Mandell, Localization theorems in topological Hochschild homology and topological cyclic homology. Available at arXiv:0802.3938.

    [2] F. Borceux, Handbook of categorical algebra. 2. Encyclopedia of Mathematics and its Applications 51 (1994). Cambridge Univ. Press.

    [3] D.-C. Cisinski, Invariance de la K-th´eorie par ´equivalences d´eriv´ees. Available at To appear in J. of K-theory.

    [4] D.-C. Cisinski and G. Tabuada, Non-connective K-theory via universal invariants. Available at arXiv:0903.3717v2.

    [5] , Symmetric monoidal structure on Non-commutative motives. Available at arXiv:1001.0228v2.

    [6] V. Drinfeld, DG quotients of DG categories. J. Algebra 272 (2004), 643-691.

    [7] A. Grothendieck, Th´eorie des intersections et th´eor`eme de Riemann-Roch. S´eminaire de G´eom´etrie Alg´ebrique du Bois-Marie 1966-1967 (SGA 6). Lecture Notes in Mathematics 225 (1971).

    [8] B. Keller, On differential graded categories. International Congress of Mathematicians (Madrid), Vol. II (2006), 151-190. Eur. Math. Soc., Zu¨rich.

    [9] , On the cyclic homology of exact categories. J. Pure Appl. Alg. 136(1) (1999), 1-56.

    [10] , On the cyclic homology of ringed spaces and schemes. Doc. Math. 3 (1998), 231-259.

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