Lagrange Resolvents Constructed from Stark Units

Beilinson–Flach elements, Stark units and 𝑝-adic iterated integrals

Forum Mathematicum ◽

10.1515/forum-2018-0281 ◽

2019 ◽

Vol 31 (6) ◽

pp. 1517-1531

Author(s):

Óscar Rivero ◽

Victor Rotger

Keyword(s):

Number Fields ◽

Euler System ◽

Iterated Integrals ◽

Special Values ◽

Weight One ◽

Stark Units

AbstractWe study weight one specializations of the Euler system of Beilinson–Flach elements introduced by Kings, Loeffler and Zerbes, with a view towards a conjecture of Darmon, Lauder and Rotger relating logarithms of units in suitable number fields to special values of the Hida–Rankin p-adic L-function. We show that the latter conjecture follows from expected properties of Beilinson–Flach elements and prove the analogue of the main theorem of Castella and Hsieh about generalized Kato classes.

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Computing Stark units for totally real cubic fields

Mathematics of Computation ◽

10.1090/s0025-5718-97-00852-1 ◽

1997 ◽

Vol 66 (219) ◽

pp. 1239-1268 ◽

Cited By ~ 8

Author(s):

David S. Dummit ◽

Jonathan W. Sands ◽

Brett A. Tangedal

Keyword(s):

Cubic Fields ◽

Stark Units ◽

Totally Real

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Iwasawa theory of Rubin-Stark units and class groups

manuscripta mathematica ◽

10.1007/s00229-016-0889-0 ◽

2016 ◽

Vol 153 (3-4) ◽

pp. 403-430 ◽

Cited By ~ 1

Author(s):

Youness Mazigh

Keyword(s):

Iwasawa Theory ◽

Class Groups ◽

Stark Units

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

International Journal of Number Theory ◽

10.1142/s1793042117500634 ◽

2017 ◽

Vol 13 (05) ◽

pp. 1165-1190 ◽

Cited By ~ 2

Author(s):

Jilali Assim ◽

Youness Mazigh ◽

Hassan Oukhaba

Keyword(s):

Number Field ◽

Finite Extension ◽

Projective Limit ◽

Ideal Class ◽

Class Groups ◽

Euler Systems ◽

Ideal Class Groups ◽

Stark Units ◽

Characteristic Ideal ◽

The Ideal

Let [Formula: see text] be a number field and let [Formula: see text] be an odd rational prime. Let [Formula: see text] be a [Formula: see text]-extension of [Formula: see text] and let [Formula: see text] be a finite extension of [Formula: see text], abelian over [Formula: see text]. In this paper we extend the classical results, e.g. [16], relating characteristic ideal of the [Formula: see text]-quotient of the projective limit of the ideal class groups to the [Formula: see text]-quotient of the projective limit of units modulo Stark units, in the non-semi-simple case, for some [Formula: see text]-irreductible characters [Formula: see text] of [Formula: see text]. The proof essentially uses the theory of Euler systems.

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