The Lifted Root Number Conjecture for some cyclic extensions of ℚ

Jürgen Ritter; Alfred Weiss

Acta Arithmetica (1999)

  • Volume: 90, Issue: 4, page 313-340
  • ISSN: 0065-1036

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Jürgen Ritter, and Alfred Weiss. "The Lifted Root Number Conjecture for some cyclic extensions of ℚ." Acta Arithmetica 90.4 (1999): 313-340. <http://eudml.org/doc/207331>.

@article{JürgenRitter1999,
author = {Jürgen Ritter, Alfred Weiss},
journal = {Acta Arithmetica},
keywords = {Galois modules; cyclotomic units; -functions; regulators; lifted root number conjecture; cyclic tame extensions},
language = {eng},
number = {4},
pages = {313-340},
title = {The Lifted Root Number Conjecture for some cyclic extensions of ℚ},
url = {http://eudml.org/doc/207331},
volume = {90},
year = {1999},
}

TY - JOUR
AU - Jürgen Ritter
AU - Alfred Weiss
TI - The Lifted Root Number Conjecture for some cyclic extensions of ℚ
JO - Acta Arithmetica
PY - 1999
VL - 90
IS - 4
SP - 313
EP - 340
LA - eng
KW - Galois modules; cyclotomic units; -functions; regulators; lifted root number conjecture; cyclic tame extensions
UR - http://eudml.org/doc/207331
ER -

References

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  1. [Bu] D. Burns, Equivariant Tamagawa numbers and Galois module theory, I, preprint, King's College London, 1997. 
  2. [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. Zbl59.0190.01
  3. [Ct] T. Chinburg, On the Galois structure of algebraic integers and S-units, Invent. Math. 74 (1983), 321-349. Zbl0564.12016
  4. [Fr] A. Fröhlich, Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields, Contemp. Math. 24, Amer. Math. Soc., 1983. Zbl0519.12001
  5. [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. Zbl1041.11075
  6. [GRW2] K. W. Gruenberg, J. Ritter and A. Weiss, On Chinburg's Root Number Conjecture, Jahresber. Deutsch. Math.-Verein. 100 (1998), 36-44. Zbl0929.11054
  7. [La] S. Lang, Cyclotomic Fields I and II, Grad. Texts in Math. 121, Springer, New York, 1990. 
  8. [RW] J. Ritter and A. Weiss, Cohomology of units and L-values at zero, J. Amer. Math. Soc. 10 (1997), 513-552. Zbl0885.11059
  9. [Ru] K. Rubin, The Main Conjecture, Appendix in [La]. 
  10. [Se] J. P. Serre, Corps Locaux, Hermann, Paris, 1968. 
  11. [Sn] V. Snaith, Galois Module Structure, Fields Inst. Monogr. 2, Amer. Math. Soc., 1994. 
  12. [Ta] J. Tate, Les Conjectures de Stark sur les Fonctions L d'Artin en s=0, Progr. Math. 47, Birkhäuser, 1984. 
  13. [Wa] L. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, 1982. 
  14. [We] A. Weiss, Multiplicative Galois Module Structure, Fields Inst. Monogr. 5, Amer. Math. Soc., 1996. 

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