Théorie d’Iwasawa des unités de Stark et groupe de classes

Assim, Jilali; Mazigh, Youness; Oukhaba, Hassan

doi:10.1142/s1793042117500634

Cited by 2 publications

(6 citation statements)

References 14 publications

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“…Since v in an infinite prime, 2H 1 Iw (K v , T) = 0 and then the characteristic ideal char(⊕ v|∞ H 1 Iw (K v , T)) is prime to J . Hence, char((A + ∞ ) χ ) is prime to J .…”

Section: The Exact Sequencementioning

confidence: 99%

“…Passing to projective limit over n, Assertion (1) follows from the proof of [1,Proposition 3.5]. In order to obtain (2), we have on the one hand the exact sequence…”

Section: The Exact Sequencementioning

confidence: 99%

“…Let O(χ ) denote the ring O on which acts via χ . For any ‫ޚ‬ Let L χ denote the fixed field of ker(χ ), and let K(1) be the maximal 2-extension inside the Hilbert class field of K. In the sequel, we will assume (for simplicity) that L = L χ and K = L ∩ K (1).…”

Section: Introduction Let K Be a Number Field And Let CL +mentioning

confidence: 99%

“…Hence, the result of [1,Proposition 3.8] does not apply, since the cohomological dimension of G K, is infinite. The second complication is the need to modify the canonical Selmer structure F can , and to study the -structure of the projective limit of these Selmer groups.…”

Section: Introduction Let K Be a Number Field And Let CL +mentioning

confidence: 99%

“…Proof. By Proposition 2.13, it suffices to prove that the -modules H 1 Iw (K, T) and H 1 Iw,+ (K, T) are -free. For this, we claim that (i) the groups…”

mentioning

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On Iwasawa Theory of Rubin–stark Units and Narrow Class Groups

Mazigh¹

2018

Glasgow Math. J.

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Let K be a totally real number field of degree r. Let K ∞ denote the cyclotomic Z 2 -extension of K and let L ∞ be a finite extension of K ∞ , abelian over K. The goal of this paper is to compare the characteristic ideal of the χ-quotient of the projective limit of the narrow class groups to the χ-quotient of the projective limit of the r-th exterior power of totally positive units modulo a subgroup of Rubin-Stark units, for some Q 2 -irreducible characters χ of Gal(L ∞ /K ∞ ).

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“…Since v in an infinite prime, 2H 1 Iw (K v , T) = 0 and then the characteristic ideal char(⊕ v|∞ H 1 Iw (K v , T)) is prime to J . Hence, char((A + ∞ ) χ ) is prime to J .…”

Section: The Exact Sequencementioning

confidence: 99%

“…Passing to projective limit over n, Assertion (1) follows from the proof of [1,Proposition 3.5]. In order to obtain (2), we have on the one hand the exact sequence…”

Section: The Exact Sequencementioning

confidence: 99%

Section: Introduction Let K Be a Number Field And Let CL +mentioning

confidence: 99%

Section: Introduction Let K Be a Number Field And Let CL +mentioning

confidence: 99%

“…Proof. By Proposition 2.13, it suffices to prove that the -modules H 1 Iw (K, T) and H 1 Iw,+ (K, T) are -free. For this, we claim that (i) the groups…”

mentioning

confidence: 99%

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