Iwasawa main conjecture for the Carlitz cyclotomic extension and applications

DOI10.1007/s00208-019-01875-8zbMath1454.11211arXiv1412.5957OpenAlexW2964652596WikidataQ122923328 ScholiaQ122923328MaRDI QIDQ2290810

Andrea Bandini, Ignazio Longhi, Francesc Bars Cortina, Bruno Anglès

Publication date: 29 January 2020

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.5957

zbMATH Keywords

Carlitz moduleclass groupsglobal function fieldsFitting idealIwaswa main conjecture

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Iwasawa theory (11R23) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items (8)

On ∞-adic and v-adic multiple zeta functions in positive characteristic ⋮ Aspects of Iwasawa theory over function fields ⋮ On Geometric Iwasawa Theory and Special Values of Zeta Functions ⋮ Stickelberger series and main conjecture for function fields ⋮ Arithmetic of function field units ⋮ On the \(\mu\)-invariants of abelian varieties over function fields of positive characteristic ⋮ Non-communtative Iwasawa main conjecture ⋮ Fitting ideals of class groups in Carlitz-Hayes cyclotomic extensions

Cites Work

• A Herbrand-Ribet theorem for function fields
• Characteristic ideals and Iwasawa theory
• Congruences between derivatives of geometric \(L\)-functions. With an appendix by David Burns, King Fai Lai and Ki-Seng Tan
• Special \(L\)-values of Drinfeld modules
• Class fields of abelian extensions of \(\mathbb Q\)
• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• Transcendence and special zeta values in characteristic p
• Iwasawa's main conjecture for elliptic curves over anticyclotonic \(\mathbb Z_p\)-extensions
• On \(L\)-functions of cyclotomic function fields
• Power sums with applications to multizeta and zeta zero distribution for \(\mathbb F_q[t\)]
• Stickelberger elements, Fitting ideals of class groups of CM-fields, and dualisation
• Dirichlet series in function fields
• On power sums of polynomials over finite fields
• The Iwasawa invariant \(\mu_p\) vanishes for abelian number fields
• \(v\)-adic zeta functions, \(L\)-series and measures for function fields
• Fitting ideals of class groups of real fields with prime power conductor
• Note on Nakayama's lemma for compact \(\Lambda\)-modules
• Formal Drinfeld modules.
• L-functions of p-adic characters and geometric Iwasawa theory
• The refined Coates-Sinnott conjecture for characteristic \(p\) global fields
• The \(\text{GL}_2\) main conjecture for elliptic curves without complex multiplication
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• Power sums of polynomials over finite fields and applications: a survey
• The Iwasawa Main Conjecture for constant ordinary abelian varieties over function fields
• The Galois Module Structure of ℓ-adic Realizations of Picard 1-motives and Applications
• CONTROL THEOREMS FOR ELLIPTIC CURVES OVER FUNCTION FIELDS
• On the Coates-Sinnott Conjecture
• Class numbers of cyclotomic function fields
• On Geometric Iwasawa Theory and Special Values of Zeta Functions
• Fitting ideals of ℓ-adic realizations of Picard 1-motives and class groups of global function fields
• Arithmetic of characteristic p special L-values
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Iwasawa main conjecture for the Carlitz cyclotomic extension and applications