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Congruences modulo between ϵ factors for cuspidal representations of G L ( 2 )

Marie-France Vignéras — 2000

Journal de théorie des nombres de Bordeaux

Let p be two different prime numbers, let F be a local non archimedean field of residual characteristic p , and let 𝐐 ¯ , 𝐙 ¯ , 𝐅 ¯ be an algebraic closure of the field of -adic numbers 𝐐 , the ring of integers of 𝐐 ¯ , the residual field of 𝐙 ¯ . We proved the existence and the unicity of a Langlands local correspondence over 𝐅 ¯ for all n 2 , compatible with the reduction modulo in [V5], without using L and ϵ factors of pairs. We conjecture that the Langlands local correspondence over 𝐐 ¯ respects congruences modulo between...

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