TY - JOUR

T1 - The local–global principle for symmetric determinantal representations of smooth plane curves in characteristic two

AU - Ishitsuka, Yasuhiro

AU - Ito, Tetsushi

N1 - Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jpaa.2016.09.013

DO - 10.1016/j.jpaa.2016.09.013

M3 - Article

AN - SCOPUS:85008674644

SN - 0022-4049

VL - 221

SP - 1316

EP - 1321

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 6

ER -