TY - JOUR
T1 - Iwasawa main conjecture for the Carlitz cyclotomic extension and applications
AU - Anglès, Bruno
AU - Bandini, Andrea
AU - Bars, Francesc
AU - Longhi, Ignazio
N1 - Funding Information:
All the authors thank the MTM 2009-10359, which funded a workshop on Iwasawa theory for function fields in 2010 and supported the authors during their stay in Barcelona in the summer of 2013, and the CRM (Centre de Recerca Matemàtica, Bellaterra, Barcelona) for providing a nice environment to work on this project. The fourth author thanks NCTS/TPE for support to travel to Barcelona in summer 2013.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - We prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field Fq(θ) (p is a prime of Fq[θ]), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a p-adic L-function to prove a close analog of the Ferrero–Washington Theorem for F and to provide information on the p-adic valuations of the Bernoulli-Goss numbers β(j) (i.e., on the values of the Carlitz-Goss ζ-function at negative integers).
AB - We prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field Fq(θ) (p is a prime of Fq[θ]), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a p-adic L-function to prove a close analog of the Ferrero–Washington Theorem for F and to provide information on the p-adic valuations of the Bernoulli-Goss numbers β(j) (i.e., on the values of the Carlitz-Goss ζ-function at negative integers).
UR - https://www.scopus.com/pages/publications/85070217638
U2 - 10.1007/s00208-019-01875-8
DO - 10.1007/s00208-019-01875-8
M3 - Article
AN - SCOPUS:85070217638
SN - 0025-5831
VL - 376
SP - 475
EP - 523
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -