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

Abstract

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.

10 pages, minor changes following the referee's suggestions; A shorter version of this paper will appear in Journal of Pure and Applied Algebra. This longer version contains an additional section (Section 4) on computational results for conics and cubics

References in corpus (3)

• Orbit parametrizations of theta characteristics on hypersurfaces over arbitrary fields
• A positive proportion of cubic curves over Q admit linear determinantal representations
• The local-global principle for symmetric determinantal representations of smooth plane curves

Cited by in corpus (1)

• Orbit parametrizations of theta characteristics on hypersurfaces over arbitrary fields