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This page goes over the construction of Greenberg schemes associated to schemes over a complete DVR, and that of Greenberg schemes associated to locally Noetherian R-adic formal schemes.
There are many things I have not included in my first pass at this article. I have not yet put much effort into emphasizing the connections between these objects and motivic integration. A more fleshed out references section is certainly in order. In terms of content, the following can (and probably should) all be added: 1. A proof of some of the assertions of representability. 2. A sketch of how Greenberg schemes generalize arc schemes. 3. Constructible subsets and measurable subsets of Greenberg schemes. 4. Motivic integration on Greenberg schemes. I will do so myself if I get around to it before anyone else happens to. Although, perhaps some of this content should be relegated to the page on motivic integration.
Charlie Conneen
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