Comodules for some simple $\mathcal O$-forms of $\mathbb G_m$

TL;DR

This paper provides a detailed description of the representation category of certain flat commutative affine group schemes over a discrete valuation ring, focusing on cases where the generic fiber is the multiplicative group.

Contribution

It offers a concrete characterization of Rep(G) for specific group schemes with multiplicative generic fiber over a discrete valuation ring.

Findings

Explicit description of the category Rep(G)

Application to simple $ ext{O}$-forms of $ ext{G}_m$

Enhanced understanding of group scheme representations

Abstract

This paper gives a rather concrete description of the category Rep(G) for certain flat commutative affine group schemes G over a discrete valuation ring such that the general fiber of G is the multiplicative group.