Congruences modulo between factors for cuspidal representations of

Marie-France Vignéras

Journal de théorie des nombres de Bordeaux (2000)

  • Volume: 12, Issue: 2, page 571-580
  • ISSN: 1246-7405

Abstract

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Let be two different prime numbers, let be a local non archimedean field of residual characteristic , and let be an algebraic closure of the field of -adic numbers , the ring of integers of , the residual field of . We proved the existence and the unicity of a Langlands local correspondence over for all , compatible with the reduction modulo in [V5], without using and factors of pairs. We conjecture that the Langlands local correspondence over respects congruences modulo between and factors of pairs, and that the Langlands local correspondence over is characterized by identities between new and factors. The aim of this short paper is prove this when .

How to cite

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Vignéras, Marie-France. "Congruences modulo $\ell $ between $\epsilon $ factors for cuspidal representations of $GL(2)$." Journal de théorie des nombres de Bordeaux 12.2 (2000): 571-580. <http://eudml.org/doc/248493>.

@article{Vignéras2000,
abstract = {Let $\ell \ne p$ be two different prime numbers, let $F$ be a local non archimedean field of residual characteristic $p$, and let $\overline\{\mathbf \{Q\}\}_\ell , \overline\{\mathbf \{Z\}\}_\ell , \overline\{\mathbf \{F\}\}_\ell $ be an algebraic closure of the field of $\ell $-adic numbers $\mathbf \{Q\}_\ell $, the ring of integers of $\overline\{\mathbf \{Q\}\}_\ell $, the residual field of $\overline\{\mathbf \{Z\}\}_\ell $. We proved the existence and the unicity of a Langlands local correspondence over $\overline\{\mathbf \{F\}\}_\ell $ for all $n \ge 2$, compatible with the reduction modulo $\ell $ in [V5], without using $L$ and $\epsilon $factors of pairs. We conjecture that the Langlands local correspondence over $\overline\{\mathbf \{Q\}\}_\ell $ respects congruences modulo $\ell $ between $L$ and $\epsilon $ factors of pairs, and that the Langlands local correspondence over $\overline\{\mathbf \{F\}\}_\ell $ is characterized by identities between new $L$ and $\epsilon $ factors. The aim of this short paper is prove this when $n = 2$.},
author = {Vignéras, Marie-France},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {local Langlands correspondence},
language = {eng},
number = {2},
pages = {571-580},
publisher = {Université Bordeaux I},
title = {Congruences modulo $\ell $ between $\epsilon $ factors for cuspidal representations of $GL(2)$},
url = {http://eudml.org/doc/248493},
volume = {12},
year = {2000},
}

TY - JOUR
AU - Vignéras, Marie-France
TI - Congruences modulo $\ell $ between $\epsilon $ factors for cuspidal representations of $GL(2)$
JO - Journal de théorie des nombres de Bordeaux
PY - 2000
PB - Université Bordeaux I
VL - 12
IS - 2
SP - 571
EP - 580
AB - Let $\ell \ne p$ be two different prime numbers, let $F$ be a local non archimedean field of residual characteristic $p$, and let $\overline{\mathbf {Q}}_\ell , \overline{\mathbf {Z}}_\ell , \overline{\mathbf {F}}_\ell $ be an algebraic closure of the field of $\ell $-adic numbers $\mathbf {Q}_\ell $, the ring of integers of $\overline{\mathbf {Q}}_\ell $, the residual field of $\overline{\mathbf {Z}}_\ell $. We proved the existence and the unicity of a Langlands local correspondence over $\overline{\mathbf {F}}_\ell $ for all $n \ge 2$, compatible with the reduction modulo $\ell $ in [V5], without using $L$ and $\epsilon $factors of pairs. We conjecture that the Langlands local correspondence over $\overline{\mathbf {Q}}_\ell $ respects congruences modulo $\ell $ between $L$ and $\epsilon $ factors of pairs, and that the Langlands local correspondence over $\overline{\mathbf {F}}_\ell $ is characterized by identities between new $L$ and $\epsilon $ factors. The aim of this short paper is prove this when $n = 2$.
LA - eng
KW - local Langlands correspondence
UR - http://eudml.org/doc/248493
ER -

References

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