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Computing the homology of Koszul complexes

By Bernhard Koeck

Abstract

Let R be a commutative ring and I an ideal in R which is locally generated by a regular sequence of length d. Then, each projective R/I-module V has an R-projective resolution P. of length d. In this paper, we compute the homology of the n-th Koszul complex associated with the homomorphism P_1 --> P_0 for all n, if d = 1. This computation yields a new proof of the classical Adams- Riemann-Roch formula for regular closed immersions which does not use the deformation to the normal cone any longer. Furthermore, if d = 2, we compute the homology of the complex N Sym^2 K(P.) where K and N denote the functors occurring in the Dold-Kan correspondence

Topics: QA
Year: 2001
OAI identifier: oai:eprints.soton.ac.uk:29783
Provided by: e-Prints Soton

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Citations

  1. (1960). Abstract description of some basic functors,
  2. (1992). Adams operations on higher K-theory,
  3. (1994). An introduction to homological algebra",
  4. (1971). Complexe Cotangent et D eformations I",
  5. (1972). Cotangent et D eformations II",
  6. (1985). e,O p erations en K-th eorie alg ebrique,
  7. (2000). for tensor powers,
  8. (1971). Grothendieck,a n dL. Illusie,\ T h eorie des Intersections et Th eor eme de Riemann-Roch",
  9. (1990). Higher algebraic K-theory of schemes and of derived categories, in:
  10. (1961). Homologie nicht-additiver Funktoren.
  11. (1960). Intrinsic characterizations of some additive functors,
  12. (1998). Linearization, Dold-Puppe stabilization, and Mac Lane's Q-construction,
  13. (1969). Manin,L e c t u r e so nt h eK-functor in algebraic geometry,
  14. (1998). ock, The Grothendieck-Riemann-Roch theorem for group scheme actions,
  15. (1954). On the groups H(;n),
  16. (1985). Riemann-Roch algebra",
  17. (1970). Riemann-Roch sans d enominateurs,
  18. (1982). Schur functors and Schur complexes,

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