Journal of Commutative Algebra

A characterization of cofinite complexes over complete Gorenstein domains

Kazufumi Eto and Ken-Ichiroh Kawasaki

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J. Commut. Algebra, Volume 3, Number 4 (2011), 537-550.

First available in Project Euclid: 8 December 2011

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Primary: 14B15: Local cohomology [See also 13D45, 32C36] 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 18G15: Ext and Tor, generalizations, Künneth formula [See also 55U25]

Local cohomology cofinite module abelian category


Eto, Kazufumi; Kawasaki, Ken-Ichiroh. A characterization of cofinite complexes over complete Gorenstein domains. J. Commut. Algebra 3 (2011), no. 4, 537--550. doi:10.1216/JCA-2011-3-4-537.

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  • S.I. Gelfant and Yu.I. Manin, Methods of Homological Algebra, Springer-Verlag, Berlin, 1996.
  • A. Grothendieck, Cohomologie locale des faisceaux cohérants et théorèmes de Lefschetz locaux et globaux (SGA 2), North-Holland, Amsterdam, 1968.
  • A. Grothendieck, Local cohomology, with notes by R. Hartshorne, Springer Lecture Notes Math. 41, Springer-Verlag, Berlin, 1967.
  • R. Hartshorne, Affine duality and cofiniteness, Invent. Math. 9 (1969/1970), 145-164.
  • –––, Residue and duality, Springer Lecture Notes Math. 20, Springer-Verlag, New York, 1966.
  • –––, Algebraic geometry, Grad. Texts Math. 52, Springer-Verlag, New York, 1977.
  • C. Huneke and J. Koh, Cofiniteness and vanishing of local cohomology modules, Math. Proc. Cambridge Philos. Soc. 110, (1991), 421-429.
  • K.-I. Kawasaki, On the finiteness of Bass numbers of local cohomology modules, Proc. Amer. Math. Soc. 124 (1996), 3275-3279.
  • –––, On a category of cofinite modules which is Abelian, Math. Z., to appear.
  • J. Lipman, Lectures on local cohomology and duality, in Local cohomology and its applications, Lect. Notes Pure Appl. Math. 226, Marcel Dekker, Inc., New York, 2002%, 39–89.
  • H. Matsumura, Commutative algebra, 2nd ed., Benjamin Cummings, Reading, Massachusetts, 1980.
  • –––, Commutative ring theory, Cambridge Stud. Adv. Math. 8, Cambridge University Press, Cambridge, 1986.
  • L. Melkersson, Properties of cofinite modules and applications to local cohomology, Math. Proc. Cambridge Philos. Soc. 125, (1999), 417-423.