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For flat modules M over a ring A we study the similarities between the three statements,dim k (P) ( k (P)? A M =dfor all prime ideals P of A, the Ap-module M p is free of rank d for all prime ideals P of A, and M is a locally free J4-module of rank d. We have particularly emphasized the case when there is an>l-algebra B, essentially of finite type, and M is a finitely generated B-module. 相似文献
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We show that the Hilbert functor of rank one families on a non-separated scheme X admits deformations that are not effective. For such ambient schemes we have that the Hilbert functor is not representable
by a scheme or an algebraic space. 相似文献
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We introduce symmetrizing operators of the polynomial ring A[x] in the variable x over a ring A. When A is an algebra over a field k these operators are used to characterize the monic polynomials F(x) of degree n in A[x] such that A
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k[x](x)/(F(x)) is a free A-module of rank n. We use the characterization to determine the Hilbert scheme parameterizing subschemes of length n of k[x](x). 相似文献
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