Title:
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Aspects of Iwasawa theory over function fields
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Author:
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Bandini, Andrea; Bars Cortina, Francesc; Longhi, Ignazio; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
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Abstract:
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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 Zdp-extensions). The final section provides more details for the cyclotomic ZNp-extension arising from the torsion of the Carlitz module: in particular, we relate cyclotomic units with Bernoulli-Carlitz numbers by a Coates-Wiles homomorphism. |
Subject(s):
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-L-funcions -Grups-Classes -Bernoulli, Nombres de |
Rights:
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open access
Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
https://creativecommons.org/licenses/by-nc-nd/3.0/ |
Document type:
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Article Prepublicació |
Published by:
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Centre de Recerca Matemàtica
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Share:
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Uri:
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https://ddd.uab.cat/record/60922
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