15. The functor of points and the Hilbert scheme Clearly a scheme
... transformations between hX and F are in natural correspondence with the elements of F (X). (2) h is an equivalence of categories with a full subcategory of Hom(C ◦ , D). Proof. Given a natural transformation α : hX −→ F, we assign the element α(iX ), where iX : X −→ X is the identity map. The invers ...
... transformations between hX and F are in natural correspondence with the elements of F (X). (2) h is an equivalence of categories with a full subcategory of Hom(C ◦ , D). Proof. Given a natural transformation α : hX −→ F, we assign the element α(iX ), where iX : X −→ X is the identity map. The invers ...
Very dense subsets of a topological space.
... Indeed, the k-rational points are the closed points, by (I, 6.4.2), and X is Jacobson. (10.4.9–11). A number of questions in algebraic geometry can be reduced to the case of a finitely generated algebra over Z or a field, so the fact that such rings are Jacobson is particularly important. EGA gives ...
... Indeed, the k-rational points are the closed points, by (I, 6.4.2), and X is Jacobson. (10.4.9–11). A number of questions in algebraic geometry can be reduced to the case of a finitely generated algebra over Z or a field, so the fact that such rings are Jacobson is particularly important. EGA gives ...
Generic Linear Algebra and Quotient Rings in Maple - CECM
... work for. For example, the Hessenberg algorithm (see [3]) computes the characteristic polynomial of a matrix of dimension n over any field F in O(n3 ) arithmetic operations. The Berkowitz algorithm (see [1]) computes the characteristic polynomial over any ring R. It is division free, and so can be a ...
... work for. For example, the Hessenberg algorithm (see [3]) computes the characteristic polynomial of a matrix of dimension n over any field F in O(n3 ) arithmetic operations. The Berkowitz algorithm (see [1]) computes the characteristic polynomial over any ring R. It is division free, and so can be a ...
