Displaying similar documents to “A generalization of level-raising congruences for algebraic modular forms”

Non-abelian congruences between L -values of elliptic curves

Daniel Delbourgo, Tom Ward (2008)

Annales de l’institut Fourier

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Let E be a semistable elliptic curve over ℚ . We prove weak forms of Kato’s K 1 -congruences for the special values L 1 , E / ℚ ( μ p n , Δ p n ) . More precisely, we show that they are true modulo p n + 1 , rather than modulo p 2 n . Whilst not quite enough to establish that there is a non-abelian L -function living in K 1 ℤ p [ [ Gal ( ℚ ( μ p ∞ , Δ p ∞ ) / ℚ ) ] ] , they do provide strong evidence towards the existence of such an analytic object. For example, if n = 1 these verify the numerical congruences found by Tim and Vladimir Dokchitser.

On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields

Matteo Longo (2006)

Annales de l’institut Fourier

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Let E / F be a modular elliptic curve defined over a totally real number field F and let φ be its associated eigenform. This paper presents a new method, inspired by a recent work of Bertolini and Darmon, to control the rank of E over suitable quadratic imaginary extensions K / F . In particular, this argument can also be applied to the cases not covered by the work of Kolyvagin and Logachëv, that is, when [ F : ℚ ] is even and φ not new at any prime.

Relative property (T) and linear groups

Talia Fernós (2006)

Annales de l’institut Fourier

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Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group Γ admits a special linear representation with non-amenable R -Zariski closure if and only if it acts on an Abelian...

Effective equidistribution of S-integral points on symmetric varieties

Yves Benoist, Hee Oh (2012)

Annales de l’institut Fourier

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Let K be a global field of characteristic not 2. Let Z = H ∖ G be a symmetric variety defined over K and S a finite set of places of K . We obtain counting and equidistribution results for the S-integral points of Z . Our results are effective when K is a number field.

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...