Aspects of Iwasawa theory over function fields
Bandini, Andrea (Università degli Studi di Parma. Dipartimento di Matematica e Informatica (Italy))
Bars Cortina, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Longhi, Ignazio (National Taiwan University. Department of Mathematics (Taiwan))

Imprint:	Zurich, Switzerland : European Mathematical Society Publishing House, 2020
Description:	31 pàg.
Abstract:	We consider ZNp-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.
Grants:	Ministerio de Ciencia e Innovación MTM2009-10359
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Language:	Anglès
Series:	EMS Series of Congress Reports
Document:	Capítol de llibre ; Versió acceptada per publicar
Subject:	Iwasawa Main Conjecture ; Global function fields ; L-functions ; Selmer groups ; Class groups ; Bernoulli-Carlitz numbers
Published in:	t-Motives: Hodge Structures, Transcendence and Other Motivic Aspects, 2020, p. 375-416, ISBN 978-3-03719-198-9

DOI: 10.4171/198-1/7

Postprint 43 p, 718.2 KB

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