Elliptic K3 surfaces with p^n-torsion sections

TL;DR

This paper classifies elliptic K3 surfaces with p^n-torsion sections in characteristic p, verifies key conjectures, and computes invariants like formal Brauer group heights and Mordell-Weil groups, especially in supersingular cases.

Contribution

It provides a complete classification of such surfaces and confirms conjectures of Artin and Shioda for p^n ≥ 3, including detailed invariant computations.

Findings

Verification of Artin and Shioda conjectures for p^n ≥ 3

Computation of formal Brauer group heights

Determination of Artin invariants and Mordell-Weil groups in supersingular cases

Abstract

We classify elliptic K3 surfaces in characteristic $p$ with $p^n$-torsion sections. For $p^n\geq3$ we verify conjectures of Artin and Shioda, compute the heights of their formal Brauer groups, as well as Artin invariants and Mordell--Weil groups in the supersingular cases.