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

Yasuhiro Ishitsuka, Tetsushi Ito

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1316-1321
Number of pages6
JournalJournal of Pure and Applied Algebra
Volume221
Issue number6
DOIs
Publication statusPublished - Jun 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'The local–global principle for symmetric determinantal representations of smooth plane curves in characteristic two'. Together they form a unique fingerprint.

Cite this