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• W3100921683 abstract "Recently, the second author has associated a finite F q [ T ] -module H to the Carlitz module over a finite extension of F q ( T ) . This module is an analogue of the ideal class group of a number field. In this paper, we study the Galois module structure of this module H for ‘cyclotomic’ extensions of F q ( T ) . We obtain function field analogues of some classical results on cyclotomic number fields, such as the p-adic class number formula, and a theorem of Mazur and Wiles about the Fitting ideal of ideal class groups. We also relate the Galois module H to Anderson's module of circular units, and give a negative answer to Anderson's Kummer–Vandiver-type conjecture. These results are based on a kind of equivariant class number formula which refines the second author's class number formula for the Carlitz module." @default.
• W3100921683 created "2020-11-23" @default.
• W3100921683 creator A5011292891 @default.
• W3100921683 creator A5063417772 @default.
• W3100921683 creator A5066718882 @default.
• W3100921683 date "2015-02-07" @default.
• W3100921683 modified "2023-10-14" @default.
• W3100921683 title "Arithmetic of characteristic p special L-values" @default.
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• W3100921683 doi "https://doi.org/10.1112/plms/pdu067" @default.
• W3100921683 hasPublicationYear "2015" @default.
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