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Displaying similar documents to “Non-abelian congruences between L -values of elliptic curves”

A generalization of level-raising congruences for algebraic modular forms

Claus Mazanti Sorensen (2006)

Annales de l’institut Fourier

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In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field F . We do this for automorphic representations of an arbitrary reductive group G over F , which is compact at infinity. In the special case where G is an inner form of GSp ( 4 ) over ℚ , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.

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...

A generalization of Scholz’s reciprocity law

Mark Budden, Jeremiah Eisenmenger, Jonathan Kish (2007)

Journal de Théorie des Nombres de Bordeaux

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We provide a generalization of Scholz’s reciprocity law using the subfields K 2 t - 1 and K 2 t of ℚ ( ζ p ) , of degrees 2 t - 1 and 2 t over ℚ , respectively. The proof requires a particular choice of primitive element for K 2 t over K 2 t - 1 and is based upon the splitting of the cyclotomic polynomial Φ p ( x ) over the subfields.

On uniform lower bound of the Galois images associated to elliptic curves

Keisuke Arai (2008)

Journal de Théorie des Nombres de Bordeaux

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Let p be a prime and let K be a number field. Let ρ E , p : G K → Aut ( T p E ) ≅ GL 2 ( ℤ p ) be the Galois representation given by the Galois action on the p -adic Tate module of an elliptic curve E over K . Serre showed that the image of ρ E , p is open if E has no complex multiplication. For an elliptic curve E over K whose j -invariant does not appear in an exceptional finite set (which is non-explicit however), we give an explicit uniform lower bound of the size of the image of ρ E , p .

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...