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Iwasawa theory for elliptic curves over imaginary quadratic fields

Massimo Bertolini — 2001

Journal de théorie des nombres de Bordeaux

Let E be an elliptic curve over ℚ , let K be an imaginary quadratic field, and let K ∞ 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 ∞ , E p ∞ ) for i = 1 , 2 , and of the p -primary Selmer group Sel p ∞ ( E / K ∞ ) , viewed as discrete modules over the Iwasawa algebra of K ∞ / K .

Regulators, L-Functions and Rational Points

Massimo Bertolini — 2013

Bollettino dell'Unione Matematica Italiana

This article is a revised version of the text of the plenary conference I gave at the XIX Congress of ``Unione Matematica Italiana'', held in Bologna in September 2011. It discusses the arithmetic significance of the values at integers of the complex and p-adic L-functions associated to Dirichlet characters and to elliptic curves.

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

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].

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