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arXiv · 1204.3535

The refined Coates-Sinnott conjecture for characteristic p global fields

Joel Dodge·Cristian Popescu
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Abstract

This article is concerned with proving a refined function field analogue of the Coates-Sinnott conjecture, formulated in the number field context in 1974. Our main theorem calculates the Fitting ideal of a certain even Quillen K-group in terms of special values of L-functions. The techniques employed are directly inspired by recent work of Greither and Popescu in the equivariant Iwasawa theory of arbitrary global fields. They rest on the results of Greither-Popescu on the Galois module structure of certain naturally defined Picard 1-motives associated to an arbitrary Galois extension of function fields.

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Joel Dodge, Cristian Popescu. 2012-04-16. The refined Coates-Sinnott conjecture for characteristic p global fields. https://arxiv.org/abs/1204.3535

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