Pencils of quadratic forms and hyperelliptic function fields

David B. Leep; Laura Mann Schueller

doi:10.1006/jabr.1999.8168

Pencils of quadratic forms and hyperelliptic function fields

David B. Leep, Laura Mann Schueller

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	532-548
Number of pages	17
Journal	Journal of Algebra
Volume	227
Issue number	2
DOIs	https://doi.org/10.1006/jabr.1999.8168
State	Published - May 15 2000

Keywords

Hyperelliptic function field
Pencil of quadratic forms
Quadratic form

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jabr.1999.8168

Cite this

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

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KW - Pencil of quadratic forms

KW - Quadratic form

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Pencils of quadratic forms and hyperelliptic function fields

Abstract

Keywords

ASJC Scopus subject areas

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