Perfect points on curves of genus 1 and consequences for supersingular K3 surfaces

[摘要] We describe a method to show that certain elliptic surfaces do not admit purely inseparable multisections (equivalently, that genus 1 curves over function fields admit no points over the perfect closure of the base field) and use it to show that any non-Jacobian elliptic structure on a very general supersingular K3 surface has no purely inseparable multisections. We also describe specific examples of genus 1 fibrations on supersingular K3 surfaces without purely inseparable multisections.

[学科分类] 数学（综合）

[关键词] supersingular K3 surface;purely inseparable point;Weierstrass fibration;Frobenius;elliptic surface;14J28;14G17