Displaying similar documents to “Hida families, p -adic heights, and derivatives”

Some new directions in p -adic Hodge theory

Kiran S. Kedlaya (2009)

Journal de Théorie des Nombres de Bordeaux

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We recall some basic constructions from p -adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of B -pairs, introduced recently by Berger, which provides a natural enlargement of the category of p -adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representations.) We also discuss results of Liu that indicate that the formalism of Galois cohomology,...

Signed Selmer groups over p -adic Lie extensions

Antonio Lei, Sarah Livia Zerbes (2012)

Journal de Théorie des Nombres de Bordeaux

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Let E be an elliptic curve over ℚ with good supersingular reduction at a prime p ≥ 3 and a p = 0 . We generalise the definition of Kobayashi’s plus/minus Selmer groups over ℚ ( μ p ∞ ) to p -adic Lie extensions K ∞ of ℚ containing ℚ ( μ p ∞ ) , using the theory of ( ϕ , Γ ) -modules and Berger’s comparison isomorphisms. We show that these Selmer groups can be equally described using Kobayashi’s conditions via the theory of overconvergent power series. Moreover, we show that such an approach gives the usual Selmer groups in the...

Anticyclotomic Iwasawa theory of CM elliptic curves

Adebisi Agboola, Benjamin Howard (2006)

Annales de l’institut Fourier

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We study the Iwasawa theory of a CM elliptic curve E in the anticyclotomic Z p -extension of the CM field, where p is a prime of good, ordinary reduction for E . When the complex L -function of E vanishes to even order, Rubin’s proof of the two variable main conjecture of Iwasawa theory implies that the Pontryagin dual of the p -power Selmer group over the anticyclotomic extension is a torsion Iwasawa module. When the order of vanishing is odd, work of Greenberg show that it is not a torsion...

p -adic Differential Operators on Automorphic Forms on Unitary Groups

Ellen E. Eischen (2012)

Annales de l’institut Fourier

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The goal of this paper is to study certain p -adic differential operators on automorphic forms on U ( n , n ) . These operators are a generalization to the higher-dimensional, vector-valued situation of the p -adic differential operators constructed for Hilbert modular forms by N. Katz. They are a generalization to the p -adic case of the C ∞ -differential operators first studied by H. Maass and later studied extensively by M. Harris and G. Shimura. The operators should be useful in the construction...

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...