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Thursday, November 4, 2010
α map being closed
Scheme.II
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Every module has a maximal submodule.
E(A/p) is p-primary
Injective embedding
UFD, irreducible elt review
gcd, lcm
UFD iff every prime of height 1 is principal, ACCP...
Nagata CM ring
Direct sum of CM modules may not be CM
Category of modules revisited
CM module definition
CM module & modding out by an ideal (A/I, I ∈ann(M))
Regular sequence and flat extension
n-th syzygy of projective resolution being projective
M^* -> M^***
Ass(Hom(M,N))=Supp(M)∩Ass(N)
Transitivity of inverse sheaf revisited, restricti...
\mathcal{F} \simeq (j_{*}\mathcal{F})|_{X}
Equivalence of categories (II)
Ringed spaces (or schemes) being a category
Bijection between Hom(V,W) and Hom_Speck(t(V),t(W)...
If W∈t(X), W is a generic point of t(W).
α map being closed
α(V) = the set of closed points in t(V)
Spec-k compatibility of the following morphisms
Restriction morphism of the second kind
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