The refined Coates-Sinnott conjecture for characteristic p global fields

JOURNAL OF NUMBER THEORY

卷:133

Article

Dodge, Joel¹  Popescu, Cristian D.² 

[1] SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA

[2] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

关键词: L-functions;    Quillen K-theory;    Etale cohomology;    Picard 1-motives;   

DOI  :  10.1016/j.jnt.2012.11.003

来源: Elsevier

【 摘 要 】

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 and Popescu on the Galois module structure of certain naturally defined Picard 1-motives associated to an arbitrary Galois extension of function fields. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free