The refined Coates-Sinnott conjecture for characteristic p global fields

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.