Sur la constante de Kummer-Leopoldt d?un corps de nombres

Assim, Jilali; Quang, Thong Nguyen

doi:10.1007/s00229-004-0482-9

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…Christian Maire gave a remark on the earlier studies on the structure of the Z p -torsion subgroup of the "group of (semi) local units modulo the completion of the group of global units". In particular, considering analogous objects of the "Kummer-Leopoldt constant" and the "p-adic normalized regulator" (see [1], [11]) seems meaningful in studying (Q2).…”

Section: X(e/k)[π]| = |X(e/k)[π]|mentioning

confidence: 99%

On the unramified Iwasawa module of a $\mathbb{Z}_p$-extension generated by division points of a CM elliptic curve

Itoh¹

2020

Preprint

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We consider the unramified Iwasawa module X(F ∞ ) of a certain Z p -extension F ∞ /F 0 generated by division points of an elliptic curve with complex multiplication. This Z p -extension has properties similar to those of the cyclotomic Z p -extension of a real abelian field, however, it is already known that X(F ∞ ) can be infinite in general. In this paper, we mainly consider analogs of weak forms of Greenberg's conjecture for F ∞ /F 0 .

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Section: X(e/k)[π]| = |X(e/k)[π]|mentioning

confidence: 99%

On the unramified Iwasawa module of a $\mathbb{Z}_p$-extension generated by division points of a CM elliptic curve

Itoh¹

2020

Preprint

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“…From [1], [11], [13], [14], [16], [17] one can study this property and its generalizations with various techniques (see the rather intricate history in [2]). Give the following definition from [2]: [14], [11] and oldest Iwasawa papers.…”

Section: The Kummer-leopoldt Constantmentioning

confidence: 99%

“…By class field theory, Gal(H pr K /H K ) ≃ U K /E K in which the image of W K fixes H reg K , the Bertrandias-Payan field, Gal(H reg K / K) being then the Bertrandias-Payan module, except possibly if p = 2 in the "special case" (cf. [2] about the calculation of κ and the Références in [6] for some history about this module). But R K giving κ K has, a priori, nothing to do with the definition of the Bertrandias-Payan module associated with p r -cyclic extensions of K, r ≥ 1, which are embeddable in cyclic p-extensions of K of arbitrary large degree.…”

Section: Interpretation Of κ K -Fundamental Exact Sequencementioning

confidence: 99%

The p-adic Kummer–Leopoldt constant: Normalized p-adic regulator

Gras¹

2018

Int. J. Number Theory

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“…It is natural to ask if this implication is in fact an equivalence (see [1], [3]). We will say that the converse of Kummer's Lemma is true for the character ρ if we have:…”

Section: The P-adic Behavior Of Jacobi Sumsmentioning

confidence: 99%

On Jacobi Sums in $\mathbb Q(ζ_p)$

Angles,

Nuccio

2008

Preprint

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We study the p-adic behavior of Jacobi sums for Q(ζ p ) and link this study to the p-Sylow subgroup of the class group of Q(ζ p ) + and to some properties of the jacobian of the Fermat curve X p + Y p = 1 over F ℓ where ℓ is a prime number distinct from p.Let p be a prime number, p ≥ 5. Iwasawa has shown that the p-adic properties of Jacobi sums for Q(ζ p ) are linked to Vandiver's Conjecture (see [5]). In this paper, we follow Iwasawa's ideas and study the p-adic properties of the subgroup J of Q(ζ p ) * generated by Jacobi sums.Let A be the p-Sylow subgroup of the class group of Q(ζ p ). If E denotes the group of units of Q(ζ p ), then if Vandiver's Conjecture is true for p, by Kummer Theory, we must have. Note that J is analoguous for the odd part to the group of cyclotomic units for the even part. We introduce a submodule W of Q(ζ p ) * which was already considered

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Sur la constante de Kummer-Leopoldt d?un corps de nombres

Cited by 5 publications

References 13 publications

On the unramified Iwasawa module of a $\mathbb{Z}_p$-extension generated by division points of a CM elliptic curve

On the unramified Iwasawa module of a $\mathbb{Z}_p$-extension generated by division points of a CM elliptic curve

The p-adic Kummer–Leopoldt constant: Normalized p-adic regulator

On Jacobi Sums in $\mathbb Q(ζ_p)$

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