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

2012/10/11 by Jeanne M. Funk, Funk, Jeanne M., Raymond T. Hoobler +1 · 1 citation
Mathematics · #19G12 (Primary) 14H99 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #math.AC #math.AG #msc:14H99 #msc:19G12

paper · pdf · doi:10.48550/arxiv.1210.3109

arxiv created 2012/10/11 · openalex publication_date 2012/10/11 · arxiv updated 2012/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we calculate the Witt ring W(C) of a smooth geometrically connected projective curve C over a finite field of characteristic different from 2. We view W(C) as a subring of W(k(C)) where k(C) is the function field of C. We show that the triviality of the Clifford algebra of a bilinear space over C gives the main relation. The calculation is then completed using classical results for bilinear spaces over fields.

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