Signed Selmer groups over $p$-adic Lie extensions

Antonio Lei; Sarah Livia Zerbes

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Displaying similar documents to “Signed Selmer groups over $p$ -adic Lie extensions”

Completely faithful Selmer groups over Kummer extensions.

Hachimori, Yoshitaka, Venjakob, Otmar (2003)

Documenta Mathematica

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On a conjecture of Watkins

Neil Dummigan (2006)

Journal de Théorie des Nombres de Bordeaux

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Watkins has conjectured that if $R$ is the rank of the group of rational points of an elliptic curve $E$ over the rationals, then $2^{R}$ divides the modular parametrisation degree. We show, for a certain class of $E$ , chosen to make things as easy as possible, that this divisibility would follow from the statement that a certain $2$ -adic deformation ring is isomorphic to a certain Hecke ring, and is a complete intersection. However, we show also that the method developed by Taylor, Wiles and others,...

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.

Towards a theory of some unbounded linear operators on $p$ -adic Hilbert spaces and applications

Toka Diagana (2005)

Annales mathématiques Blaise Pascal

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We are concerned with some unbounded linear operators on the so-called $p$ -adic Hilbert space $𝔼_{ω}$ . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on $𝔼_{ω}$ , and the solvability of the equation $A u = v$ where $A$ is a linear operator on $𝔼_{ω}$ .

A note on some expansions of p-adic functions

Grzegorz Szkibiel (1992)

Acta Arithmetica

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Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by ${(ϕ ₘ)}_{m \in ℕ ₀}$ . The system ${(ϕ ₘ)}_{m \in ℕ ₀}$ is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to ${(ϕ ₘ)}_{m \in ℕ ₀}$ . This paper is a remark to Rutkowski’s paper. We define another system ${(h ₙ)}_{n \in ℕ ₀}$ in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski....

The integral logarithm in Iwasawa theory : an exercise

Jürgen Ritter, Alfred Weiss (2010)

Journal de Théorie des Nombres de Bordeaux

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Let $l$ be an odd prime number and $H$ a finite abelian $l$ -group. We describe the unit group of $Λ_{\land} [H]$ (the completion of the localization at $l$ of $ℤ_{l} [[T]] [H]$ ) as well as the kernel and cokernel of the integral logarithm $L : Λ_{\land} {[H]}^{\times} \to Λ_{\land} [H]$ , which appears in non-commutative Iwasawa theory.

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...

Displaying similar documents to “Signed Selmer groups over p -adic Lie extensions”

Completely faithful Selmer groups over Kummer extensions.

On a conjecture of Watkins

Integrable functions for the Bernoulli measures of rank 1

Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications

A note on some expansions of p-adic functions

The integral logarithm in Iwasawa theory : an exercise

Anticyclotomic Iwasawa theory of CM elliptic curves

Displaying similar documents to “Signed Selmer groups over $p$ -adic Lie extensions”

Integrable functions for the Bernoulli measures of rank $1$

Towards a theory of some unbounded linear operators on $p$ -adic Hilbert spaces and applications