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

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.