I'm not an expert in scheme theory, so I just ask this question to understand some peculiarity of this language. The situation I was thinking about is really concrete. Let me consider a group scheme $G$ over a Dedekind ring $A$, think about the ring of integers of some number field. Suppose we completely know all the connected components of the fibers of this group scheme over all primes of $A$ and over the generic point of $A$. Is it possible to construct a subgroup scheme of $G$, whose fibers over the primes and the generic point interpolate all these connected components? By interpolation I mean that all the base change of this group subscheme must be the connected components found before. Is there any reference for such a problem? Thanks in advance for any suggestion!
2026-03-25 22:09:40.1774476580
Reconstructing a subscheme from fibers
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