GENERALIZED SECTION FUNCTORS

[摘要] The aim of this paper is - for any ideal a of a commutative noetherian ring A - to introduce and study a functor GAMMA(a)(X, Y) of two complexes X and Y of A-modules. If X = A (the ring A considered as a complex concentrated in degree zero), then GAMMA(a)(X, Y) = GAMMA(a)(Y), the usual section functor with support in V(a) introduced by Grothendieck. When X = M and Y = N are A-modules then it turns out that the cohomology module H(i)(GAMMA(a)(X, Y)) is naturally isomorphic to the generalized local cohomology module H(a)i(M, N), which was introduced by J. Herzog. Furthermore, it turns out that the functor GAMMA(a)(-, A) is isomorphic to the duality functor D(a)(-) introduced by Hartshorne when A is a regular ring.

[发布日期] 1994-07-25