The Witt ring of a curve with good reduction over a non-dyadic local field

JOURNAL OF ALGEBRA

卷:422

Article

Funk, Jeanne M.¹  Hoobler, Raymond T.² 

[1] LaGuardia Community Coll, Dept Math Engn & Comp Sci, Long Isl City, NY 11101 USA

[2] CUNY, Grad Ctr, Math Program, New York, NY 10016 USA

关键词: Witt ring;    Fundamental ideal;    Bilinear forms;    Curves over local fields;    Brauer group;   

DOI  :  10.1016/j.jalgebra.2014.07.035

来源: Elsevier

【 摘 要 】

In this work, we present a generalization to varieties and sheaves of the fundamental ideal of the Witt ring of a field by defining a sheaf of fundamental ideals (I) over tilde and a sheaf of Witt rings (W) over tilde in the obvious way. The Milnor conjecture then relates the associated graded of (W) over tilde to Milnor K-theory and so allows the classical invariants of a bilinear space over a field to be extended to our setting using etale cohomology. As an application of these results, we calculate the Witt ring of a smooth curve with good reduction over a non-dyadic local field. (C) 2014 Published by Elsevier Inc.

【 授权许可】

Free