# On the structure of affine flat group schemes over discrete valuation rings

## TL;DR

This paper investigates the structure of affine flat group schemes over discrete valuation rings using Neron blowups and Tannakian categories, and explores their role in the degeneration of differential Galois groups of -modules.

## Contribution

It introduces a novel approach combining Neron blowups and Tannakian categories to analyze affine group schemes over discrete valuation rings and their impact on differential Galois groups.

## Key findings

- Characterization of affine flat group schemes over DVRs.
- Application of Tannakian categories to differential Galois theory.
- Insights into the degeneration behavior of differential Galois groups.

## Abstract

We study affine group schemes over a discrete valuation ring $R$ using two techniques: Neron blowups and Tannakian categories. We employ the theory developed to define and study differential Galois groups of $\mathcal D$-modules on a scheme over a $R$. This throws light on how differential Galois groups of families degenerate.