منابع مشابه
P-class Groups of Certain Extensions of Degree P
Let p be an odd prime number. In this article we study the distribution of p-class groups of cyclic number fields of degree p, and of cyclic extensions of degree p of an imaginary quadratic field whose class number is coprime to p. We formulate a heuristic principle predicting the distribution of the p-class groups as Galois modules, which is analogous to the Cohen-Lenstra heuristics concerning...
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Let F be a global field of characteristic p > 0, F/F a Galois extension with Gal(F/F ) ≃ Z l (for some prime l 6= p) and E/F a non-isotrivial elliptic curve. We study the behaviour of Selmer groups SelE(L)r (r any prime) as L varies through the subextensions of F via appropriate versions of Mazur’s Control Theorem. With mild hypotheses on SelE(F )r (essentially a consequence of the Birch and Sw...
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Let p be an odd prime number, E an elliptic curve over a number field k, and F/k a Galois extension of degree twice a power of p. We study the Zp-corank rkp(E/F ) of the p-power Selmer group of E over F . We obtain lower bounds for rkp(E/F ), generalizing the results in [MR], which applied to dihedral extensions. If K is the (unique) quadratic extension of k in F , G = Gal(F/K), G is the subgro...
متن کاملOn the Structure of Selmer Groups of Λ-Adic Deformations over p-Adic Lie Extensions
In this paper, we consider the Λ-adic deformations of Galois representations associated to elliptic curves. We prove that the Pontryagin dual of the Selmer group of a Λ-adic deformation over certain p-adic Lie extensions of a number field, that are not necessarily commutative, has no non-zero pseudo-null submodule. We also study the structure of various arithmetic Iwasawa modules associated to ...
متن کاملMULTIPLE Z p - EXTENSIONS
Let A be the inverse limit of the p-part of the ideal class groups in a Zpextension K∞/K. Greenberg conjectures that if r is maximal, then A is pseudo-null as a module over the Iwasawa algebra Λ (that is, has codimension at least 2). We prove this conjecture in the case that K is the field of p-th roots of unity, p has index of irregularity 1, satisfies Vandiver’s conjecture, and satisfies a mi...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2017
ISSN: 0024-6107
DOI: 10.1112/jlms.12038