Displaying similar documents to “An annihilator for the p -Selmer group by means of Heegner points”

Iwasawa theory for elliptic curves over imaginary quadratic fields

Massimo Bertolini (2001)

Journal de théorie des nombres de Bordeaux

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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 . ...

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...

Artinian cofinite modules over complete Noetherian local rings

Behrouz Sadeghi, Kamal Bahmanpour, Jafar A'zami (2013)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R -module. In this paper it is shown that if 𝔭 is a prime ideal of R such that dim R / 𝔭 = 1 and ( 0 : M 𝔭 ) is not finitely generated and for each i ≥ 2 the R -module Ext R i ( M , R / 𝔭 ) is of finite length, then the R -module Ext R 1 ( M , R / 𝔭 ) is not of finite length. Using this result, it is shown that for all finitely generated R -modules N with Supp ( N ) ⊆ V ( I ) and for all integers i ≥ 0 , the R -modules Ext R i ( N , M ) are of finite length, if and only if, for all finitely generated R -modules...

Galois module structure of the rings of integers in wildly ramified extensions

Stephen M. J. Wilson (1989)

Annales de l'institut Fourier

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The main results of this paper may be loosely stated as follows. Theorem.— Let N and N ' be sums of Galois algebras with group Γ over algebraic number fields. Suppose that N and N ' have the same dimension ℚ and that they are identical at their wildly ramified primes. Then (writing 𝒪 N for the maximal order in N ) 𝒪 N ⊕ 𝒪 N ⊕ ℤ Γ ≅ ℤ Γ ⊕ 𝒪 N ' ⊕ 𝒪 N ' ⊕ ℤ Γ .

Some results on the cofiniteness of local cohomology modules

Sohrab Sohrabi Laleh, Mir Yousef Sadeghi, Mahdi Hanifi Mostaghim (2012)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring, 𝔞 an ideal of R , M an R -module and t a non-negative integer. In this paper we show that the class of minimax modules includes the class of 𝒜ℱ modules. The main result is that if the R -module Ext R t ( R / 𝔞 , M ) is finite (finitely generated), H 𝔞 i ( M ) is 𝔞 -cofinite for all i < t and H 𝔞 t ( M ) is minimax then H 𝔞 t ( M ) is 𝔞 -cofinite. As a consequence we show that if M and N are finite R -modules and H 𝔞 i ( N ) is minimax for all i < t then the set of associated prime ideals of the generalized local cohomology...