The local–global principle for symmetric determinantal representations of smooth plane curves

Yasuhiro Ishitsuka, Tetsushi Ito

研究成果: ジャーナルへの寄稿学術誌査読

2 被引用数 (Scopus)

抄録

A smooth plane curve is said to admit a symmetric determinantal representation if it can be defined by the determinant of a symmetric matrix with entries in linear forms in three variables. We study the local–global principle for the existence of symmetric determinantal representations of smooth plane curves over a global field of characteristic different from two. When the degree of the plane curve is less than or equal to three, we relate the problem of finding symmetric determinantal representations to more familiar Diophantine problems on the Severi–Brauer varieties and mod 2 Galois representations, and prove that the local–global principle holds for conics and cubics. We also construct counterexamples to the local–global principle for quartics using the results of Mumford, Harris, and Shioda on theta characteristics.

本文言語英語
ページ(範囲)141-162
ページ数22
ジャーナルRamanujan Journal
43
1
DOI
出版ステータス出版済み - 5月 1 2017
外部発表はい

!!!All Science Journal Classification (ASJC) codes

  • 代数と数論

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