Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T12:25:21.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Evidence for a Conjectural Generalization of Hilbert's Theorem 132

Published online by Cambridge University Press:  01 February 2010

W. Bley
W. Bley
Affiliation:
Institut für Mathematik, Universität Augsburg, Universitätsstrasse 8, D-86135 Augsburg, [email protected], http://www.math.uni-augsburg.de/~bley

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper presents an algorithm for computing numerical evidence for a conjecture whose validity is predicted by the requirement that the equivariant Tamagawa number conjectures for Tate motives as formulated by Burns and Flach are compatible with the functional equation of the Artin L-series. The algorithm includes methods for the computation of Fitting ideals and projective lattices over the integral group ring.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 6 , 2003 , pp. 68 - 88
Copyright
Copyright © London Mathematical Society 2003

References

1Batut, C., Belabas, K., Bernardi, D., Cohen, H. and Olivier, M., ‘User's guide to PARI⁄GP’, 2000; http://www.parigp-home.de.Google Scholar
2Bley, W., ‘Computing associated orders and Galois generating elements of unit lattices’, J. Number Theory 62 (1997) 242–256.CrossRefGoogle Scholar
3Bley, W. and Burns, D., ‘Étale cohomology and a generalisation of Hilbert's theorem 132’, Math. Z. 239 (2002) 1–25.CrossRefGoogle Scholar
4Bley, W. and Burns, D., ‘Equivariant epsilon constants, discriminants and étale cohomology’, J. London Math. Soc, to appear.Google Scholar
5Breuning, M. ‘On equivariant global epsilon constants for certian dihedral extesnsions’, Math. Comp., to appear.Google Scholar
6Burns, D., ‘Equivariant Tamagawa numbers and Galois module theory I’, Compositio Math. 129 (2001) 203–237.Google Scholar
7Burns, D., ‘Equivariant Tamagawa numbers and Galois module theory II’, preprint, 1998.Google Scholar
8Burns, D. and Flach, M., ‘On Galois structure invariants associated to Tate motives’, Amer. J. Math. 120 (1998) 1343–1397.CrossRefGoogle Scholar
9Chinburg, T., ‘On the Galois structure of algebraic integers and S-units’, Invent. Math. 74 (1983) 321–349.Google Scholar
10Cohen, H., A course in computational algebraic number theory, Grad. Texts in Math. 138 (Springer, Berlin⁄Heidelberg⁄New York, 1995).Google Scholar
11Cohen, H., Advanced topics in computational number theory, Grad. Texts in Math. 193 (Springer, New York⁄Berlin⁄Heidelberg, 2000).CrossRefGoogle Scholar
12Curtis, C. and Reiner, I., Methods of representation theory, vol. I, Wiley Classics Library (Wiley, New York⁄Chichester⁄Brisbane⁄Toronto, 1994).Google Scholar
13Erez, B., ‘A survey of recent work on the square root of the inverse different’, Journées arithmétiques, Exp.Congr., Luminy⁄Fr. 1989, Astérisque 198–200 (1991) 133–152.Google Scholar
14Fröhlich, A., Galois module structure of algebraic integers (Springer, Heidelberg, 1983).CrossRefGoogle Scholar
15Fröhlich, A., ‘L-values at zero and multiplicative Galois module structure (also Galois-Gauss sums and additive Galois module structure)’, J. Reine Angew. Math. 397 (1989) 42–99.CrossRefGoogle Scholar
16Hilbert, D., ‘Die Theorie der algebraischen Zahlkörper’, Jahresber. Deutsch. Math. -Verein. 4(1897).Google Scholar
17Knudsen, F. and Mumford, D., ‘The projectivity of the moduli space of stable curves I: Preliminaries on “det” and “Div”’, Math. Scand. 39 (1976) 19–55.CrossRefGoogle Scholar
18Martinet, J., ‘Character theory and Artin L-functions’, Algebraic number fields (ed. Fröhlich, A., Academic Press, 1977).Google Scholar
19Mazur, B. and Wiles, A., ‘Class fields of abelian extensions of ’, Invent. Math. 76 (1984) 179–330.Google Scholar
20Neukirch, J., Algebraische Zahlentheorie (Springer, Heidelberg, 1992).CrossRefGoogle Scholar
21Popescu, C., ‘On a refined Stark conjecture for function fields’, Compositio Math. 116 (1999) 321–367.CrossRefGoogle Scholar
22Roblot, X. F., ‘Algorithmes de factorisation dans les extensions relatives et application de la conjecture de Stark à la construction des corps de classes de rayon’, Thesis, Université Bordeaux I, 1997.Google Scholar
23Washington, L., Introduction to cyclotomic fields, Grad. Texts in Math. 83 (Springer, New York⁄Heidelberg⁄Berlin, 1982).Google Scholar
Supplementary material: File

JCM 6 Bley Appendix B Part 1

Bley Appendix B Part 1

Download JCM 6 Bley Appendix B Part 1(File)
File 95.6 KB
Supplementary material: File

JCM 6 Bley Appendix B Part 2

Bley Appendix B Part 2

Download JCM 6 Bley Appendix B Part 2(File)
File 7.8 KB