A class–field theoretical calculation

Cristian D. Popescu[1]

  • [1] University of California, San Diego, Department of Mathematics 9500 Gilman Drive La Jolla, CA 92093-0112, USA

Journal de Théorie des Nombres de Bordeaux (2006)

  • Volume: 18, Issue: 2, page 477-486
  • ISSN: 1246-7405

Abstract

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In this paper, we give the complete characterization of the p –torsion subgroups of certain idèle–class groups associated to characteristic p function fields. As an application, we answer a question which arose in the context of Tan’s approach [6] to an important particular case of a generalization of a conjecture of Gross [4] on special values of L –functions.

How to cite

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Popescu, Cristian D.. "A class–field theoretical calculation." Journal de Théorie des Nombres de Bordeaux 18.2 (2006): 477-486. <http://eudml.org/doc/249653>.

@article{Popescu2006,
abstract = {In this paper, we give the complete characterization of the $p$–torsion subgroups of certain idèle–class groups associated to characteristic $p$ function fields. As an application, we answer a question which arose in the context of Tan’s approach [6] to an important particular case of a generalization of a conjecture of Gross [4] on special values of $L$–functions.},
affiliation = {University of California, San Diego, Department of Mathematics 9500 Gilman Drive La Jolla, CA 92093-0112, USA},
author = {Popescu, Cristian D.},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Class–field theory; Galois cohomology; class field theory},
language = {eng},
number = {2},
pages = {477-486},
publisher = {Université Bordeaux 1},
title = {A class–field theoretical calculation},
url = {http://eudml.org/doc/249653},
volume = {18},
year = {2006},
}

TY - JOUR
AU - Popescu, Cristian D.
TI - A class–field theoretical calculation
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2006
PB - Université Bordeaux 1
VL - 18
IS - 2
SP - 477
EP - 486
AB - In this paper, we give the complete characterization of the $p$–torsion subgroups of certain idèle–class groups associated to characteristic $p$ function fields. As an application, we answer a question which arose in the context of Tan’s approach [6] to an important particular case of a generalization of a conjecture of Gross [4] on special values of $L$–functions.
LA - eng
KW - Class–field theory; Galois cohomology; class field theory
UR - http://eudml.org/doc/249653
ER -

References

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  1. E. Artin, J. Tate, Class–field Theory. Addison–Wesley Publishing Co., Inc.- Advanced Book Classics Series, 1990. Zbl0681.12003MR1043169
  2. K. Brown, Cohomology of Groups. GTM 87, Springer Verlag, 1982. Zbl0584.20036MR672956
  3. J.W.S. Cassels, A. Fröhlich, Editors, Algebraic Number Theory. Academic Press, London and New York, 1967. Zbl0153.07403MR215665
  4. B.H. Gross, On the values of abelian L –functions at s = 0 . Jour. Fac. Sci. Univ. Tokyo 35 (1988), 177–197. Zbl0681.12005MR931448
  5. H. Kisilevsky, Multiplicative independence in function fields. Journal of Number Theory 44 (1993), 352–355. Zbl0780.11058MR1233295
  6. K.S. Tan, Generalized Stark formulae over function fields, preprint. Zbl1233.11117
  7. K.S. Tan, Private Communication, 2001–2002. 
  8. J. Tate, Les conjectures de Stark sur les fonctions L d’Artin en s = 0 . Progr. in Math. 47, Boston Birkhäuser, 1984 . Zbl0545.12009MR782485

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