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A criterion for Greenberg's conjecture
Author(s):
Luca
Caputo;
Filippo
Alberto Edoardo
Nuccio
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2741-2744.
MSC (2000):
Primary 11R23;
Secondary 11R70
Posted:
April 3, 2008
MathSciNet review:
2399036
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Abstract:
We give a criterion for the vanishing of the Iwasawa  -invariants of totally real number fields  based on the class number of  by evaluating the  -adic  -functions at  .
References:
-
- [BN]
- R. BADINO AND T. NGUYEN QUANG DO, Sur les égalités du miroir et certaines formes faibles de la conjecture de Greenberg, Manuscripta Mathematica, CXVI, 323-340 (2005). MR 2130946 (2006b:11133)
- [Gra]
- G. GRAS, Class field theory: From theory to practice, Springer Monographs in Mathematics, Springer-Verlag, 2003. MR 1941965 (2003j:11138)
- [Gre]
- C. GREITHER, Class groups of abelian fields, and the main conjecture, Annales de l'Institut Fourier, XLII, 449-499 (1992). MR 1182638 (93j:11071)
- [Was]
- L. WASHINGTON, Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, Vol. 83, Springer-Verlag, 1997. MR 1421575 (97h:11130)
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Additional Information:
Luca
Caputo
Affiliation:
Dipartimento di Matematica ``Leonida Tonelli'', Università degli studi di Pisa, Largo Bruno Pontecorvo, 5 - 56127 - Pisa, Italy
Email:
caputo@mail.dm.unipi.it
Filippo
Alberto Edoardo
Nuccio
Affiliation:
Dipartimento di Matematica ``Guido Castelnuovo'', Università degli studi ``La Sapienza'' Piazzale Aldo Moro, 5 - 00185 - Roma, Italy
Email:
nuccio@mat.uniroma1.it
DOI:
10.1090/S0002-9939-08-09283-6
PII:
S 0002-9939(08)09283-6
Keywords:
Iwasawa theory,
Greenberg's Conjecture,
$K$-theory of Global Fields
Received by editor(s):
June 8, 2007,
Received by editor(s) in revised form:
July 2, 2007
Posted:
April 3, 2008
Additional Notes:
The second author wishes to thank the ``Laboratoire de Mathématiques Nicolas Oresme'' de Caen for its kind hospitality during the period in which this work has been done.
Communicated by:
Ken Ono
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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