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A note on trilinear forms for reducible representations and Beilinson's conjectures

Michael Harris, Anthony Scholl (2001)

Journal of the European Mathematical Society

We extend Prasad’s results on the existence of trilinear forms on representations of G L 2 of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic cohomology of the product of two modular curves constructed by Beilinson.

B dR -représentations dans le cas relatif

Fabrizio Andreatta, Olivier Brinon (2010)

Annales scientifiques de l'École Normale Supérieure

Dans ce travail nous développons un analogue relatif de la théorie de Sen pour les B dR -représentations. On donne des applications à la théorie des représentations p -adiques, en la reliant à la théorie des ( ϕ , Γ ) -modules relatifs, et à celle des modules de Higgs p -adiques développée par G. Faltings.

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

Marie-France Vignéras (2000)

Journal de théorie des nombres de Bordeaux

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

Davenport-Hasse relations and an explicit Langlands correspondence, II : twisting conjectures

Colin J. Bushnell, Guy Henniart (2000)

Journal de théorie des nombres de Bordeaux

Let F / ℚ p be a finite field extension. The Langlands correspondence gives a canonical bijection between the set 𝒢 F 0 ( n ) of equivalence classes of irreducible n -dimensional representations of the Weil group 𝒲 F of F and the set 𝒜 F 0 ( n ) of equivalence classes of irreducible supercuspidal representations of GL n ( F ) . This paper is concerned with the case where n = p m . In earlier work, the authors constructed an explicit bijection π : 𝒢 F 0 ( p m ) → 𝒜 F 0 ( p m ) using a non-Galois tame base change map. If this tame base change satisfies a certain conjectured...

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