Skip to main content
SpringerLink
Log in

The excess intersection formula for Grothendieck–Witt groups

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

We prove the excess intersection and self intersection formulae for Grothendieck–Witt groups.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balmer, P.: Witt groups. In: Handbook of K-theory, vol. 1, 2, pp. 539–576. Springer, Berlin (2005)

  2. Balmer P., Gille S.: Koszul complexes and symmetric forms over the punctured affine space. Proc. Lond. Math. Soc. (3) 91(2), 273–299 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Calmès, B., Hornbostel, J.: Push-forwards for witt groups of schemes. Preprint available at http://arxiv.org/pdf/0806.0571 (2008)

  4. Déglise F.: Interprétation motivique de la formule d’excès d’intersection. C. R. Math. Acad. Sci. Paris 338(1), 41–46 (2004)

    MATH  MathSciNet  Google Scholar 

  5. Fasel J., Srinivas V.: Chow-Witt groups and Grothendieck-Witt groups of regular schemes. Adv. Math. 221(1), 302–329 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fulton, W.: Intersection theory, volume 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 2nd edn. Springer-Verlag, Berlin (1998)

  7. Gille S.: Homotopy invariance of coherent Witt groups. Math. Z. 244(2), 211–233 (2003)

    MATH  MathSciNet  Google Scholar 

  8. Gille S., Hornbostel J.: A zero theorem for the transfer of coherent Witt groups. Math. Nachr. 278(7–8), 815–823 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gille S., Nenashev A.: Pairings in triangular Witt theory. J. Algebra 261(2), 292–309 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hartshorne, R.: Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne. Lecture notes in mathematics, No. 20. Springer-Verlag, Berlin (1966)

  11. Hartshorne, R.: Algebraic Geometry. Springer-Verlag, New York (1977). Graduate Texts in Mathematics, No. 52

  12. Köck B.: Das Adams-Riemann-Roch-Theorem in der höheren äquivarianten K-Theorie. J. Reine Angew. Math. 421, 189–217 (1991)

    MATH  MathSciNet  Google Scholar 

  13. Lipman, J.: Notes on derived functors and Grothendieck duality. Notes available at http://www.math.purdue.edu/~lipman/Duality.pdf (2008)

  14. Matsumura, H.: Commutative Algebra. W. A. Benjamin, Inc., New York (1970)

  15. Nenashev A.: Gysin maps in Balmer-Witt theory. J. Pure Appl. Algebra 211(1), 203–221 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Quillen, D.: Higher algebraic K-theory. I. In: Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), pp. 85–147. Lecture Notes in Math., vol. 341. Springer, Berlin, (1973)

  17. Rost M.: Chow groups with coefficients. Doc. Math. 1(16), 319–393 (1996) (electronic)

    MATH  MathSciNet  Google Scholar 

  18. Schlichting, M.: Hermitian k-theory, derived equivalences and karoubi’s fundamental theorem. Preprint available at http://www.math.lsu.edu/~mschlich/research/prelim.html (2008)

  19. Walter, C.: Grothendieck-Witt groups of projective bundles. Preprint available at www.math.uiuc.edu/K-theory/0644/ (2003)

  20. Walter, C. Grothendieck-Witt groups of triangulated categories. Preprint available at www.math.uiuc.edu/K-theory/0643/ (2003)

Download references

Author information

Authors and Affiliations

  1. 1984 Mathematics Road, UBC, Vancouver, BC, V6T 1Z2, Canada

    Jean Fasel

Authors
  1. Jean Fasel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jean Fasel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fasel, J. The excess intersection formula for Grothendieck–Witt groups. manuscripta math. 130, 411–423 (2009). https://doi.org/10.1007/s00229-009-0300-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-009-0300-5

Mathematics Subject Classification (2000)

Search

Navigation