Displaying similar documents to “Iwasawa theory for elliptic curves over imaginary quadratic fields”

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

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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].

On the classgroups of imaginary abelian fields

David Solomon (1990)

Annales de l'institut Fourier

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Let p be an odd prime, χ an odd, p -adic Dirichlet character and K the cyclic imaginary extension of Q associated to χ . We define a “ χ -part” of the Sylow p -subgroup of the class group of K and prove a result relating its p -divisibility to that of the generalized Bernoulli number B 1 , χ - 1 . This uses the results of Mazur and Wiles in Iwasawa theory over Q . The more difficult case, in which p divides the order of χ is our chief concern. In this case the result is new and confirms an earlier conjecture...

Precobalanced and cobalanced sequences of modules over domains

Anthony Giovannitti, H. Pat Goeters (2007)

Mathematica Bohemica

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The class of pure submodules ( 𝒫 ) and torsion-free images ( ℛ ) of finite direct sums of submodules of the quotient field of an integral domain were first investigated by M. C. R. Butler for the ring of integers (1965). In this case 𝒫 = ℛ and short exact sequences of such modules are both prebalanced and precobalanced. This does not hold for integral domains in general. In this paper the notion of precobalanced sequences of modules is further investigated. It is shown that as in the case for...