Skip to main content
SpringerLink
Log in

CM–fields and skew–symmetric matrices

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract.

Cohen and Odoni prove that every CM–field can be generated by an eigenvalue of some skew–symmetric matrix with rational coefficients. It is natural to ask for the minimal dimension of such a matrix. They show that every CM–field of degree 2n is generated by an eigenvalue of a skew–symmetric matrix over Q of dimension at most 4n+2. The aim of the present paper is to improve this bound.

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. Bayer–Fluckiger, E.: Ideal lattices. Proceedings of the Conference Number Theory and Diophantine Geometry: Baker 60, Zürich (1999), Cambridge University Press, 2002, pp. 168–184

  2. Bender, E.A.: Characteristic polynomials of symmetric matrices. Pacific J. Math. 25, 433–441 (1968)

    MATH  Google Scholar 

  3. Berhuy, G.: On hermitian trace forms over hilbertian fields. Math. Z. 217, 561–570 (2001)

    MathSciNet  Google Scholar 

  4. Cohen, S.D., Odoni, R.W.K.: Galois groups associated with CM–fields, skew–symmetric matrices and orthogonal matrices. Glasgow Math. J. 32, 35–46 (1990)

    MathSciNet  MATH  Google Scholar 

  5. Krüskemper, M.: On the scaled trace forms and the transfer of a number field extension. J. Number Th. 40, 105–119 (1992)

    MathSciNet  Google Scholar 

  6. Scharlau, W.: Quadratic and Hermitian Forms, Grundlehren Math. Wiss. 270, Springer Verlag, 1985

Download references

Author information

Authors and Affiliations

  1. Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    Eva Bayer-Fluckiger

  2. Department of Mathematics, University of British Columbia, Vancouver BC, V6S 1C2, Canada

    Grégory Berhuy

  3. Institut de Mathématiques, Université de Neuchâtel, rue Emile Argand 11, 2007, Neuchâtel, Switzerland

    Pascale Chuard–Koulmann

Authors
  1. Eva Bayer-Fluckiger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Grégory Berhuy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pascale Chuard–Koulmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eva Bayer-Fluckiger.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bayer-Fluckiger, E., Berhuy, G. & Chuard–Koulmann, P. CM–fields and skew–symmetric matrices. manuscripta math. 114, 351–359 (2004). https://doi.org/10.1007/s00229-004-0462-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-004-0462-0

Keywords

Search

Navigation