Local ε 0 -characters in torsion rings

Seidai Yasuda[1]

  • [1] Research Institute for Mathematical Sciences Kyoto University Kyoto 606-8502, Japan

Journal de Théorie des Nombres de Bordeaux (2007)

  • Volume: 19, Issue: 3, page 763-797
  • ISSN: 1246-7405

Abstract

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Let p be a rational prime and K a complete discrete valuation field with residue field k of positive characteristic p . When k is finite, generalizing the theory of Deligne [1], we construct in [10] and [11] a theory of local ε 0 -constants for representations, over a complete local ring with an algebraically closed residue field of characteristic ≠ p , of the Weil group W K of K . In this paper, we generalize the results in [10] and [11] to the case where k is an arbitrary perfect field.

How to cite

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Yasuda, Seidai. "Local $\varepsilon _0$-characters in torsion rings." Journal de Théorie des Nombres de Bordeaux 19.3 (2007): 763-797. <http://eudml.org/doc/249970>.

@article{Yasuda2007,
abstract = {Let $p$ be a rational prime and $K$ a complete discrete valuation field with residue field $k$ of positive characteristic $p$. When $k$ is finite, generalizing the theory of Deligne [1], we construct in [10] and [11] a theory of local $\varepsilon _0$-constants for representations, over a complete local ring with an algebraically closed residue field of characteristic $\ne p$, of the Weil group $W_K$ of $K$. In this paper, we generalize the results in [10] and [11] to the case where $k$ is an arbitrary perfect field.},
affiliation = {Research Institute for Mathematical Sciences Kyoto University Kyoto 606-8502, Japan},
author = {Yasuda, Seidai},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {local constants; Galois representations; Weil group},
language = {eng},
number = {3},
pages = {763-797},
publisher = {Université Bordeaux 1},
title = {Local $\varepsilon _0$-characters in torsion rings},
url = {http://eudml.org/doc/249970},
volume = {19},
year = {2007},
}

TY - JOUR
AU - Yasuda, Seidai
TI - Local $\varepsilon _0$-characters in torsion rings
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2007
PB - Université Bordeaux 1
VL - 19
IS - 3
SP - 763
EP - 797
AB - Let $p$ be a rational prime and $K$ a complete discrete valuation field with residue field $k$ of positive characteristic $p$. When $k$ is finite, generalizing the theory of Deligne [1], we construct in [10] and [11] a theory of local $\varepsilon _0$-constants for representations, over a complete local ring with an algebraically closed residue field of characteristic $\ne p$, of the Weil group $W_K$ of $K$. In this paper, we generalize the results in [10] and [11] to the case where $k$ is an arbitrary perfect field.
LA - eng
KW - local constants; Galois representations; Weil group
UR - http://eudml.org/doc/249970
ER -

References

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  1. P. Deligne, Les constantes des équations fonctionnelles des fonctions L , Modular functions in one variable II. Lecture Notes in Math. 349, 501–597. Springer, Berlin, 1973. Zbl0271.14011MR349635
  2. P. Deligne, Les constantes locales de l’équation fonctionnelle de la fonction L d’Artin d’une représentation orthogonale. Invent. Math. 35 (1976), 299–316. Zbl0337.12012MR506172
  3. M. Hazewinkel, Corps de classes local, appendix of M. Demazure, P. Gabriel, Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs, 648–681. Masson & Cie, Éditeur, Paris; North-Holland Publishing Co., Amsterdam, 1970. Zbl0203.23401MR302656
  4. G. Laumon, Transformation de Fourier, constantes d’équations fonctionnelles et conjecture de Weil. Inst. Hautes Études Sci. Publ. Math. 65 (1987), 131–210. Zbl0641.14009MR908218
  5. T. Saito, Ramification groups and local constants. UTMS preprint 96-19, University of Tokyo (1996). 
  6. J.-P. Serre, Groupes proalgébriques. Inst. Hautes Études Sci. Publ. Math. 7 (1960), 1–67. Zbl0097.35901MR118722
  7. J.-P. Serre, Zeta and L functions. Arithmetical Algebraic Geometry, 82–92. Harper and Row, New York, 1965. Zbl0171.19602MR194396
  8. J.-P. Serre, Représentations linéaires des groupes finis. Hermann, Paris, 1967. Zbl0189.02603MR232867
  9. J.-P. Serre, Corps locaux. Hermann, Paris, 1968. MR354618
  10. S. Yasuda, Local constants in torsion rings. Preprint (2001). Zbl1251.11078MR2582036
  11. S. Yasuda, The product formula for local constants in torsion rings. Preprint (2001). Zbl1251.11079MR2582037

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