Displaying similar documents to “ p -adic Differential Operators on Automorphic Forms on Unitary Groups”

Ordinary p -adic Eisenstein series and p -adic L -functions for unitary groups

Ming-Lun Hsieh (2011)

Annales de l’institut Fourier

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The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for GL 2 × 𝒦 × by the method of Eisenstein congruence on G U ( 3 , 1 ) , where 𝒦 is an imaginary quadratic field. We construct a p -adic family of ordinary Eisenstein series on the group of unitary similitudes G U ( 3 , 1 ) with the constant term which is basically the product of the Kubota-Leopodlt p -adic L -function and a p -adic L -function for GL 2 × 𝒦 × . This construction also provides a different point of view of p -adic...

Hida families, p -adic heights, and derivatives

Trevor Arnold (2010)

Annales de l’institut Fourier

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This paper concerns the arithmetic of certain p -adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a p -adic regulator, and the derivative of a p -adic L -function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions,...

Geometric and p -adic Modular Forms of Half-Integral Weight

Nick Ramsey (2006)

Annales de l’institut Fourier

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In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define p -adic modular forms of half-integral weight and to construct p -adic Hecke operators.

A finiteness result for the compactly supported cohomology of rigid analytic varieties, II

Roland Huber (2007)

Annales de l’institut Fourier

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Let h : X → Y be a separated morphism of adic spaces of finite type over a non-archimedean field k with Y affinoid and of dimension ≤ 1 , let L be a locally closed constructible subset of X and let g : ( X , L ) → Y be the morphism of pseudo-adic spaces induced by h . Let A be a noetherian torsion ring with torsion prime to the characteristic of the residue field of the valuation ring of k and let F be a constant A -module of finite type on ( X , L ) e ´ t . There is a natural class 𝒞 ( Y ) of A -modules on Y e ´ t generated by the constructible...