The Witt Ring of a Smooth Projective Curve Over a Finite Field

Abstract

In this paper, we calculate the Witt ring W(C) of a smooth geometrically connected projective curve C over a finite field with characteristic other than 2. We view W(C) as a subring of W(k(C)) where k(C) is the function field of C. The calculation is then completed using classical results for bilinear spaces over fields.

Key Words:

• Bilinear forms
• Brauer group
• Curves over finite fields
• Witt ring

2010 Mathematics Subject Classification:

• 11G20
• 11E81

Notes

Communicated by A. Wadsworth.