We prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field F-q (theta) (p is a prime of F-q [theta]), 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 beta(j) (i.e., on the values of the Carlitz-Goss zeta-function at negative integers).
Iwasawa main conjecture for the Carlitz cyclotomic extension and applications
Ignazio Longhi
2020-01-01
Abstract
We prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field F-q (theta) (p is a prime of F-q [theta]), 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 beta(j) (i.e., on the values of the Carlitz-Goss zeta-function at negative integers).File in questo prodotto:
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