“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
Paper IPM / M / 8434  


Abstract:  
Let R be a commutative Noetherian ring, \frak a an ideal of
R and N an Rmodule. We prove that, for every finitely
generated Rmodule of finite projective dimension t, the
elements in the support of generalized local cohomology module
H^{n+t}_{\frak a}(M, N) of height n is finite for all n\geqslant 0. This implies that, if R is a ddimensional local
ring, then H^{d+t−1}_{\frak a}(M, N) has finite support for
arbitrary R, \frak a and N. In addition, for a
nonnegative integer n, we show that if M and N are
arbitrary finitely generated Rmodules such that the Rmodules
H^{i}_{\frak a}( N) and H^{i}_{\frak a}(M, N) have finite
support for all i < n, then Ass H^{n}_{\frak a}(M, N) is
finite.
Download TeX format 

back to top 