Characteristic ideals and Selmer groups

Bandini, Andrea; Bars, Francesc; Longhi, Ignazio

doi:10.1016/j.jnt.2015.05.011

Cited by 7 publications

(12 citation statements)

References 24 publications

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“…for any χ of type 3 (note that we actually have equality for characters of type 1 and 2) and this is enough to have a compatible inverse system of ideals and to define their inverse limit inside Λ[[G F ]] (a similar procedure has been used in [2] and [3] for characteristic ideals).…”

Section: 1mentioning

confidence: 99%

Fitting ideals of class groups in Carlitz–Hayes cyclotomic extensions

Bandini

Bars

Coscelli

2022

Journal of Number Theory

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We generalize some results of Greither and Popescu to a geometric Galois cover X → Y which appears naturally for example in extensions generated by p n -torsion points of a rank 1 normalized Drinfeld module (i.e. in subextensions of Carlitz-Hayes cyclotomic extensions of global fields of positive characteristic). We obtain a description of the Fitting ideal of class groups (or of their dual) via a formula involving Stickelberger elements and providing a link (similar to the one in [1]) with Goss ζ-function.

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Section: 1mentioning

confidence: 99%

Fitting ideals of class groups in Carlitz–Hayes cyclotomic extensions

Bandini

Bars

Coscelli

2022

Journal of Number Theory

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“…A generalization of the torsion statement for Z d p -extensions containing F arit can be found in [59] and [8] (where one also finds an approach to the results of Section 3 in terms of characteristic ideals).…”

Section: λ-Modules and Fitting Idealsmentioning

confidence: 99%

Aspects of Iwasawa theory over function fields

Bandini¹,

Bars²,

Longhi³

2020

$T$-Motives: Hodge Structures, Transcendence and Other Motivic Aspects

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We consider Z N p -extensions F of a global function field F and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the number fields case as well. When dealing with the Selmer group of an abelian variety A defined over F , we provide all the ingredients to formulate an Iwasawa Main Conjecture relating the Fitting ideal and the p-adic L-function associated to A and F. We do the same, with characteristic ideals and p-adic L-functions, in the case of class groups (using known results on characteristic ideals and Stickelberger elements for Z d p -extensions). The final section provides more details for the cyclotomic Z N p -extension arising from the torsion of the Carlitz module: in particular, we relate cyclotomic units with Bernoulli-Carlitz numbers by a Coates-Wiles homomorphism.

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“…The interpolation formula (1) as well as the explicit expression of * A,L,ω are the content of Theorem 4.7, while (2) is proved in Theorem 4.9. The p-adic L-function L A,L ∈ Λ is defined to be a product of twists of the Stickelberger element associated to L/K (see (30)).…”

Section: Introductionmentioning

confidence: 96%

“…It is worthwhile to mention that over function fields we have Z d p -extensions for arbitrarily large d. Our result has been used by Burns and Kakde [3] for the non-commutative situation. See also [1] for another application.…”

Section: Introductionmentioning

confidence: 99%