Perfect Closures of Rings and Schemes1
نویسندگان
چکیده
0. In [3], Serre has defined the notion of a perfect variety over a field of characteristic p>0. Of course, a perfect variety is, in general, not a variety. The appropriate setting is that of schemes [2]. We show how to construct the perfect closure of a scheme, in particular, of a ring A, of characteristic p. This amounts to showing that the functor 5—>Ylom(A, B) is representable in the category of perfect rings. We do this by the technique of inductive limits.
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