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

Compositio mathematica

article

Daniel Bragg¹  Max Lieblich² 

[1] Evans Hall, University of California;Padelford Hall, University of Washington

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

DOI  :  10.1112/S0010437X22007382

学科分类：数学（综合）

来源: Cambridge University Press

【 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.

【 授权许可】

CC BY