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

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 D-modules on a scheme over a $R$. This throws light on how differential Galois groups of families degenerate. We show that a certain class of affine group schemes of "infinite type", Neron blowups of formal subgroups, are quite typical. We also explain how these group schemes appear naturally in Tannakian categories of D-modules. To conclude we isolate a Tannakian property of affine group schemes which allows one to verify if its coordinate ring is projective over the base ring.