✦ LIBER ✦

Pencils of Quadratic Forms and Hyperelliptic Function Fields

✍ Scribed by David B. Leep; Laura Mann Schueller

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 126 KB
Volume: 227
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8168

No coin nor oath required. For personal study only.

✦ Synopsis

Let P k denote the set of equivalence classes of nonsingular pencils of Ž . quadratic forms of even order defined over a field k, char k / 2. Let F k denote the set of k-isomorphism classes of hyperelliptic function fields defined over k. We Ž . Ž . define a map ⌽: P k ª F k and determine precisely when ⌽ is surjective and when ⌽ is injective. This extends a method used by A. Weil to study pairs of quadratic forms over finite fields.

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