Selmer groups and Heegner points in anticyclotomic $\mathbb {Z}_p$-extensions

Massimo Bertolini

Displaying similar documents to “Selmer groups and Heegner points in anticyclotomic $ℤ_{p}$ -extensions”

On the Iwasawa theory of CM elliptic curves at supersingular primes

Gary McConnell (1996)

Compositio Mathematica

Similarity:

Iwasawa theory for elliptic curves over imaginary quadratic fields

Massimo Bertolini (2001)

Journal de théorie des nombres de Bordeaux

Similarity:

Let $E$ be an elliptic curve over $ℚ$ , let $K$ be an imaginary quadratic field, and let $K_{\infty}$ be a $ℤ_{p}$ -extension of $K$ . Given a set $Σ$ of primes of $K$ , containing the primes above $p$ , and the primes of bad reduction for $E$ , write $K_{Σ}$ for the maximal algebraic extension of $K$ which is unramified outside $Σ$ . This paper is devoted to the study of the structure of the cohomology groups $H^{i} (K_{Σ} / K_{\infty}, E_{p^{\infty}})$ for $i = 1, 2,$ and of the $p$ -primary Selmer group Sel $_{p^{\infty}} (E / K_{\infty})$ , viewed as discrete modules over the Iwasawa algebra of $K_{\infty} / K .$ ...

$p$ -adic representations arising from descent on abelian varieties

Michael Harris (1979)

Compositio Mathematica

Similarity:

An annihilator for the $p$ -Selmer group by means of Heegner points

Massimo Bertolini (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Let $E / Q$ be a modular elliptic curve, and let $K$ be an imaginary quadratic field. We show that the $p$ -Selmer group of $E$ over certain finite anticyclotomic extensions of $K$ , modulo the universal norms, is annihilated by the «characteristic ideal» of the universal norms modulo the Heegner points. We also extend this result to the anticyclotomic $Z_{p}$ -extension of $K$ . This refines in the current contest a result of [1].

Duality theorems for $Γ$ -extensions of algebraic number fields

Kay Wingberg (1985)

Compositio Mathematica

Similarity:

The work of Mazur and Wiles on cyclotomic fields

John Coates (1980-1981)

Séminaire Bourbaki

Similarity:

Euler system for Galois deformations

Tadashi Ochiai (2005)

Annales de l’institut Fourier

Similarity:

In this paper, we develop the Euler system theory for Galois deformations. By applying this theory to the Beilinson-Kato Euler system for Hida’s nearly ordinary modular deformations, we prove one of the inequalities predicted by the two-variable Iwasawa main conjecture. Our method of the proof of the Euler system theory is based on non-arithmetic specializations. This gives a new simplified proof of the inequality between the characteristic ideal of the Selmer group of a Galois deformation...

Displaying similar documents to “Selmer groups and Heegner points in anticyclotomic ℤ p -extensions”

On the Iwasawa theory of CM elliptic curves at supersingular primes

Iwasawa theory for elliptic curves over imaginary quadratic fields

p -adic representations arising from descent on abelian varieties

An annihilator for the p -Selmer group by means of Heegner points

Duality theorems for Γ -extensions of algebraic number fields

The work of Mazur and Wiles on cyclotomic fields

Euler system for Galois deformations

Displaying similar documents to “Selmer groups and Heegner points in anticyclotomic $ℤ_{p}$ -extensions”

$p$ -adic representations arising from descent on abelian varieties

An annihilator for the $p$ -Selmer group by means of Heegner points

Duality theorems for $Γ$ -extensions of algebraic number fields