Finite flat models of constant group schemes of rank two

TL;DR

This paper computes the number of finite flat models of rank two constant group schemes over ramified p-adic fields by analyzing the rational points on a moduli space.

Contribution

It introduces a method to count isomorphism classes of finite flat models using moduli space point counting, providing explicit enumeration in a ramified setting.

Findings

Explicit count of isomorphism classes over ramified p-adic fields

Development of a moduli space approach for finite flat models

Application to rank two constant group schemes

Abstract

We calculate the number of the isomorphism class of the finite flat models over the ring of integers of an absolutely ramified $p$-adic field of constant group schemes of rank two over finite fields, by counting the rational points of a moduli space of finite flat models.