Group schemes of period 2

TL;DR

This paper constructs an explicit duality between finite flat commutative group schemes of period 2 over 2-adic valuation rings and algebraically closed residue fields, extending previous work for p>2.

Contribution

It provides a new explicit antiequivalence for period 2 group schemes, expanding the understanding of their structure over 2-adic fields.

Findings

Explicit construction of the antiequivalence

Extension of previous methods to period 2

Broader understanding of group schemes over 2-adic rings

Abstract

We give an explicit construction of the antiequivalence of the category of finite flat commutative group schemes of period 2 defined over the valuation ring of a 2-adic field with algebraically closed residue field. This result extends the earlier author's approach to group schemes of period p>2 from Proceedings of LMS, 101, 2010, 207-259.