Displaying similar documents to “On non-abelian Stark-type conjectures”

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...

Non-existence and splitting theorems for normal integral bases

Cornelius Greither, Henri Johnston (2012)

Annales de l’institut Fourier

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We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower ℚ ⊂ K ⊂ L forces the tower to be split in a very strong sense.

Annihilators of minus class groups of imaginary abelian fields

Cornelius Greither, Radan Kučera (2007)

Annales de l’institut Fourier

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For certain imaginary abelian fields we find annihilators of the minus part of the class group outside the Stickelberger ideal. Depending on the exact situation, we use different techniques to do this. Our theoretical results are complemented by numerical calculations concerning borderline cases.

An explicit formula for the Hilbert symbol of a formal group

Floric Tavares Ribeiro (2011)

Annales de l’institut Fourier

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A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ( ϕ , Γ )-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ( ϕ , Γ )-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas...

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,...