Displaying similar documents to “Some new directions in p -adic Hodge theory”

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,...

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...

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...

Integrable functions for the Bernoulli measures of rank 1

Hamadoun Maïga (2010)

Annales mathématiques Blaise Pascal

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In this paper, following the p -adic integration theory worked out by A. F. Monna and T. A. Springer [, ] and generalized by A. C. M. van Rooij and W. H. Schikhof [, ] for the spaces which are not σ -compacts, we study the class of integrable p -adic functions with respect to Bernoulli measures of rank 1 . Among these measures, we characterize those which are invertible and we give their inverse in the form of series.

The Heisenberg uncertainty relation in harmonic analysis on p -adic numbers field

Cui Minggen, Zhang Yanying (2005)

Annales mathématiques Blaise Pascal

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In this paper, two important geometric concepts–grapical center and width, are introduced in p -adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in p -adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on p -adic numbers field.