Abstract
The construction of these groups is straightforward; to an algebra B we assign the quotient R,,, G,/G,. The main effort comes in showing that these are the only possibilities. The key to this, and the basic technical idea in the paper, is the use of N&on blow-ups of group schemes over valuation rings. This process has been used before [ 1, 21 as a tool for resolving singularities, but in fact it also furnishes a good grasp on the structure of models in general. A further instance of this is found in the last section, where we give an analysis of all models (smooth or not) of G, over a valuation ring. It seems likely that the technique should also have other applications.
Published Version
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