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Pàgina inicial > Articles > Articles publicats > Iwasawa main conjecture for the Carlitz cyclotomic extension and applications |
Data: | 2020 |
Resum: | 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). |
Ajuts: | Ministerio de Economía y Competitividad MTM2016-75980-P |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió sotmesa a revisió |
Matèria: | Stickelberger series ; Carlitz-Goss ζ-function ; L-functions ; Bernoulli-Goss numbers ; Class groups ; Iwasawa Main Conjecture ; Function fields ; Cyclotomic extensions |
Publicat a: | Mathematische Annalen, Vol. 376, Issue 1-2 (February 2020) , p. 475-523, ISSN 1432-1807 |
Preprint 36 p, 438.1 KB |