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| Paper IPM / M / 8434 |
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| Abstract: | |
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Let R be a commutative Noetherian ring, \frak a an ideal of
R and N an R-module. We prove that, for every finitely
generated R-module of finite projective dimension t, the
elements in the support of generalized local cohomology module
Hn+t\frak a(M, N) of height n is finite for all n\geqslant 0. This implies that, if R is a d-dimensional local
ring, then Hd+t−1\frak a(M, N) has finite support for
arbitrary R, \frak a and N. In addition, for a
non-negative integer n, we show that if M and N are
arbitrary finitely generated R-modules such that the R-modules
Hi\frak a( N) and Hi\frak a(M, N) have finite
support for all i < n, then Ass Hn\frak a(M, N) is
finite.
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