Geodesic
VANISHING OF (CO)HOMOLOGY OVER DEFORMATIONS OF COHEN-MACAULAY LOCAL RINGS OF MINIMAL MULTIPLICITY
Glasgow mathematical journal, Tome 61 (2019) no. 3, pp. 705-725

Voir la notice de l'article provenant de la source Cambridge

DOI

Let R be a d-dimensional Cohen–Macaulay (CM) local ring of minimal multiplicity. Set S := R/(f), where f := f1,. . .,fc is an R-regular sequence. Suppose M and N are maximal CM S-modules. It is shown that if ExtSi(M, N) = 0 for some (d + c + 1) consecutive values of i ⩾ 2, then ExtSi(M, N) = 0 for all i ⩾ 1. Moreover, if this holds true, then either projdimR(M) or injdimR(N) is finite. In addition, a counterpart of this result for Tor-modules is provided. Furthermore, we give a number of necessary and sufficient conditions for a CM local ring of minimal multiplicity to be regular or Gorenstein. These conditions are based on vanishing of certain Exts or Tors involving homomorphic images of syzygy modules of the residue field. 
GHOSH, DIPANKAR; PUTHENPURAKAL, TONY J. VANISHING OF (CO)HOMOLOGY OVER DEFORMATIONS OF COHEN-MACAULAY LOCAL RINGS OF MINIMAL MULTIPLICITY. Glasgow mathematical journal, Tome 61 (2019) no. 3, pp. 705-725. doi: 10.1017/S0017089518000459
@article{10_1017_S0017089518000459,
     author = {GHOSH, DIPANKAR and PUTHENPURAKAL, TONY J.},
     title = {VANISHING {OF} {(CO)HOMOLOGY} {OVER} {DEFORMATIONS} {OF} {COHEN-MACAULAY} {LOCAL} {RINGS} {OF} {MINIMAL} {MULTIPLICITY}},
     journal = {Glasgow mathematical journal},
     pages = {705--725},
     year = {2019},
     volume = {61},
     number = {3},
     doi = {10.1017/S0017089518000459},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000459/}
}
TY  - JOUR
AU  - GHOSH, DIPANKAR
AU  - PUTHENPURAKAL, TONY J.
TI  - VANISHING OF (CO)HOMOLOGY OVER DEFORMATIONS OF COHEN-MACAULAY LOCAL RINGS OF MINIMAL MULTIPLICITY
JO  - Glasgow mathematical journal
PY  - 2019
SP  - 705
EP  - 725
VL  - 61
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000459/
DO  - 10.1017/S0017089518000459
ID  - 10_1017_S0017089518000459
ER  - 
%0 Journal Article
%A GHOSH, DIPANKAR
%A PUTHENPURAKAL, TONY J.
%T VANISHING OF (CO)HOMOLOGY OVER DEFORMATIONS OF COHEN-MACAULAY LOCAL RINGS OF MINIMAL MULTIPLICITY
%J Glasgow mathematical journal
%D 2019
%P 705-725
%V 61
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000459/
%R 10.1017/S0017089518000459
%F 10_1017_S0017089518000459

Cité par Sources :