The local-global principle for symmetric determinantal representations of smooth plane curves in characteristic two

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• 作者：Yasuhiro Ishitsuka ^{yasu-ishi@math.kyoto-u.ac.jp} ; Tetsushi Ito ; ^{tetsushi@math.kyoto-u.ac.jp}
• 关键词：Primary ; 14H50 ; secondary ; 11D41 ; 14F22 ; 14G17 ; 14K15 ; 14K30
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：221
• 期：6
• 页码：1316-1321
• 全文大小：271 K
• 卷排序：221

文摘

We give an application of Mumford's theory of canonical theta characteristics to a Diophantine problem in characteristic two. We prove that a smooth plane curve over a global field of characteristic two is defined by the determinant of a symmetric matrix with entries in linear forms in three variables if and only if such a symmetric determinantal representation exists everywhere locally. It is a special feature in characteristic two because analogous results are not true in other characteristics.