Finiteness Properties of Formal Local Cohomology Modules and Cohen–Macaulayness

REFERENCES

• Asgharzadeh , M. , Divaani-Aazar , K. , Tousi , M. ( 2009 ). Finiteness dimension of local cohomology modules and its dual notion . J. Pure Appl. Algebra 213 : 321 – 328 .
   Web of Science ®Google Scholar
• Bijan-Zadeh , M. H. ( 1980 ). A common generalization of local cohomology theories . Glasgow Math. J. 21 : 173 – 181 .
   Google Scholar
• Brodmann , M. , Sharp , R. Y. ( 1998 ). Local Cohomology: An Algebraic Introduction with Geometric Applications . Vol. 60 . Cambridge : Cambridge University Press .
   Google Scholar
• Delfino , D. , Marley , T. ( 1997 ). Cofinite modules and local cohomology . J. Pure Appl. Algebra 121 : 45 – 52 .
   Web of Science ®Google Scholar
• Divaani-Aazar , K. , Hajikarimi , A. Generalized local cohomology modules and homological Gorenstein dimensions . To appear in Comm. Algebra.
   Google Scholar
• Divaani-Aazar , K. , Sazeedeh , R. ( 2004 ). Cofiniteness of generalized local cohomology modules . Colloq. Math. 99 : 283 – 290 .
   Google Scholar
• Divaani-Aazar , K. , Naghipour , R. , Tousi , M. ( 2002 ). Cohomological dimension of certain algebraic varieties . Proc. Amer. Math. Soc. 130 : 3537 – 3544 .
   Web of Science ®Google Scholar
• Divaani-Aazar , K. , Tousi , M. ( 1999 ). Some remarks on coassociated primes . J. Korean Math. Soc. 36 : 847 – 853 .
   Google Scholar
• Hellus , M. ( 2005 ). On the associated primes of Matlis duals of top local cohomology modules . Comm. Algebra 33 : 3997 – 4009 .
   Web of Science ®Google Scholar
• Hellus , M. ( 2008 ). A note on the injective dimension of local cohomology modules . Proc. Amer. Math. Soc. 136 : 2313 – 2321 .
   Web of Science ®Google Scholar
• Hellus , M. ( 2007 ). Local Cohomology and Matlis Duality. Habilitationsschrift, Universität Leipzig .
   Google Scholar
• Hellus , M. , Schenzel , P. ( 2008 ). On cohomologically complete intersections . J. Algebra 320 : 3733 – 3748 .
   Web of Science ®Google Scholar
• Herzog , J. ( 1974 ). Komplexe Auflösungen und Dualität in der Lokalen Algebra. Habilitationsschrift, Universität Regensburg .
   Google Scholar
• Hochster , M. , Eagon , J. A. ( 1971 ). Cohen–Macaulay rings, invariant theory, and the generic perfection of determinantal loci . Amer. J. Math. 93 : 1020 – 1058 .
   Web of Science ®Google Scholar
• Huneke , C. , Koh , J. ( 1991 ). Cofiniteness and vanishing of local cohomology modules . Math. Proc. Cambridge Philos. Soc. 110 : 421 – 429 .
   Web of Science ®Google Scholar
• Huneke , C. , Sharp , R. Y. ( 1993 ). Bass numbers of local cohomology modules . Trans. Amer. Math. Soc. 339 : 765 – 779 .
   Web of Science ®Google Scholar
• Illusie , L. ( 2005 ). Grothendieck's existence theorem in formal geometry . In: Fundamental Algebraic Geometry, Mathematical Surveys and Monographs . Vol. 123 . Providence , RI : American Mathematical Society, pp . 179 – 234 .
   Google Scholar
• Kawasaki , K. I. ( 1998 ). Cofiniteness of local cohomology modules for principal ideals . Bull. London Math. Soc. 30 : 241 – 246 .
   Web of Science ®Google Scholar
• Kempf , G. ( 1979 ). The Hochster–Roberts theorem of invariant theory . Michigan Math. J. 26 : 19 – 32 .
   Web of Science ®Google Scholar
• Lyubeznik , G. ( 1993 ). Finiteness properties of local cohomology modules (an application of D-modules to commutative algebra) . Invent. Math. 113 : 41 – 55 .
   Web of Science ®Google Scholar
• Melkersson , L. (1999). Properties of cofinite modules and applications to local cohomology. Math. Proc. Cambridge Philos. Soc. 125:417–423.
   Web of Science ®Google Scholar
• Melkersson , L. ( 1995 ). Cohomological properties of modules with secondary representations . Math. Scand. 77 : 197 – 208 .
   Google Scholar
• Ogus , A. ( 1973 ). Local cohomological dimension of algebraic varieties . Ann. Math. 98 : 327 – 365 .
   Web of Science ®Google Scholar
• Peskine , C. , Szpiro , L. Dimension projective finie et cohomologie locale . Publ. Math. I.H.E.S. 42 : 47 – 119 .
   Google Scholar
• Rotman , J. ( 1979 ). An Introduction to Homological Algebra . San Diego : Academic Press .
   Google Scholar
• Schenzel , P. ( 2007 ). On formal local cohomology and connectedness . J. Algebra 315 : 894 – 923 .
   Web of Science ®Google Scholar
• Stückrad , J. , Vogel , W. ( 1986 ). Buchsbaum Rings and Applications . Berlin : Springer-Verlag .
   Google Scholar
• Vasconcelos , W. V. ( 1974 ). Divisor Theory in Module Categories, Vol. 14. North-Holland Mathematics Studies .
   Google Scholar
• Yoshida , K. I. ( 1997 ). Cofiniteness of local cohomology modules for ideals of dimension one . Nagoya Math. J. 147 : 179 – 191 .
   Web of Science ®Google Scholar
• Zöschinger , H. ( 1994 ). Der Krullsche Durchschnittssatz für kleine Untermoduln . Arch. Math. (Basel) 62 : 292 – 299 .
   Web of Science ®Google Scholar
• Communicated by A. Singh.
   Google Scholar