The Lifted Root Number Conjecture for some cyclic extensions of ℚ

• Autorzy: Jürgen Ritter , Alfred Weiss
• Języki publikacji: EN

Kategorie tematyczne

• 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers
• 11R37: Class field theory
• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 90
• Numer: 4
• Strony: 313-340

Daty

wydano

1999

otrzymano

1998-06-22

poprawiono

1998-10-01

Twórcy

autor

Jürgen Ritter

• Institut für Mathematik, Universität Augsburg, D-86135 Augsburg, Germany

autor

Alfred Weiss

• Department of Mathematics, University of Alberta, Edmonton T6G 2G1, Canada

Bibliografia

• [Bu] D. Burns, Equivariant Tamagawa numbers and Galois module theory, I, preprint, King's College London, 1997.
• [Cc] C. Chevalley, Sur la théorie du corps de classes dans les corps finis et les corps locaux, J. Fac. Sci. Tokyo 2 (1933), 365-476.
• [Ct] T. Chinburg, On the Galois structure of algebraic integers and S-units, Invent. Math. 74 (1983), 321-349.
• [Fr] A. Fröhlich, Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields, Contemp. Math. 24, Amer. Math. Soc., 1983.
• [GRW1] K. W. Gruenberg, J. Ritter and A. Weiss, A local approach to Chinburg's Root Number Conjecture, Proc. London Math. Soc. 79 (1999), 47-80.
• [GRW2] K. W. Gruenberg, J. Ritter and A. Weiss, On Chinburg's Root Number Conjecture, Jahresber. Deutsch. Math.-Verein. 100 (1998), 36-44.
• [La] S. Lang, Cyclotomic Fields I and II, Grad. Texts in Math. 121, Springer, New York, 1990.
• [RW] J. Ritter and A. Weiss, Cohomology of units and L-values at zero, J. Amer. Math. Soc. 10 (1997), 513-552.
• [Ru] K. Rubin, The Main Conjecture, Appendix in [La].
• [Se] J. P. Serre, Corps Locaux, Hermann, Paris, 1968.
• [Sn] V. Snaith, Galois Module Structure, Fields Inst. Monogr. 2, Amer. Math. Soc., 1994.
• [Ta] J. Tate, Les Conjectures de Stark sur les Fonctions L d'Artin en s=0, Progr. Math. 47, Birkhäuser, 1984.
• [Wa] L. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, 1982.
• [We] A. Weiss, Multiplicative Galois Module Structure, Fields Inst. Monogr. 5, Amer. Math. Soc., 1996.