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another typo
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tim-at-topos committed Sep 12, 2024
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\p{
Let #{X_0} be a scheme of finite type over the field #{k}, and suppose that #{X_0} is \em{simple} (by which we mean \em{absolutely} simple) over #{k}, but not necessarily proper over #{k}.
Let #{A} be a local Artinian ring with residue field #{k}.
We are interested in finding schemes #{X} that are flat over #{A}, and such that #{X\otimes_A k=X_0} (this is the starting point of the "_theory of modules_", or of "structure variations" of #{X_0}).
We are interested in finding schemes #{X} that are flat over #{A}, and such that #{X\otimes_A k=X_0} (this is the starting point of the "\em{theory of modules}", or of "structure variations" of #{X_0}).
\oldpage{182-12}
It is equivalent to give either such an #{X} or, on the topological space #{X_0}, a sheaf #{\OO_X} endowed with the following structures:

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