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  • Volume 2 (2010)
  • no. 2
  • p. 123-126
The category of cofinite modules for ideals of dimension one and codimension one
Ken-ichiroh Kawasaki
Actes des rencontres du CIRM, Volume 2 (2010) no. 2, p. 123-126
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Published online : 2011-10-20
DOI : https://doi.org/10.5802/acirm.48
Classification:  14B15,  13D03,  18G15
Keywords: Abelian category, Derived category, Cofinite complex, Cofinite module
@article{ACIRM_2010__2_2_123_0,
     author = {Ken-ichiroh Kawasaki},
     title = {The category of cofinite modules for ideals of dimension one and codimension one},
     journal = {Actes des rencontres du CIRM},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     pages = {123-126},
     doi = {10.5802/acirm.48},
     language = {en},
     url = {https://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_123_0}
}
Kawasaki, Ken-ichiroh. The category of cofinite modules for ideals of dimension one and codimension one. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 123-126. doi : 10.5802/acirm.48. https://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_123_0/
  • References

[1] K. Eto and K. -i. Kawasaki, A characterization of cofinite complexes over complete Gorenstein domains, to appear in Journal of Commutative Algebra.

[2] D. Delfino and T. Marley, Cofinite modules and local cohomology, Journal Pure and Applied Algebra, 121 (1997), 45–52.

[3] A. Grothendieck, Local Cohomology, noted by R. Hartshorne, Springer Lecture note in Mathematics, No. 41, Springer-Verlag, Berlin, Heidelberg, New York, (1967).

[4] A. Grothendieck, Cohomologie locale des faisceaux cohérants et théorèmes de Lefschetz locaux et globaux (SGA 2), North-Holland, Amsterdam, (1968).

[5] R. Hartshorne, Affine duality and cofiniteness, Inventiones Mathematicae, 9 (1970), 145–164.

[6] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, 52, Springer-Verlag, New York Berlin Heidelberg, (1977).

[7] R. Hartshorne, Residue and Duality, Springer Lecture note in Mathematics, No. 20, Springer-Verlag, New York, Berlin, Heidelberg, (1966).

[8] C. Huneke and J. Koh, Cofiniteness and vanishing of local cohomology modules, Mathematical Proceedings of the Cambridge Philosophical Society, 110 No. 3 (1991), 421–429.

[9] K. -i. Kawasaki, On a category of cofinite modules for principal ideals, preprint.

[10] K. -i. Kawasaki, On finiteness properties of local cohomology modules over Cohen-Macaulay local rings, Illinois Journal of Mathematics, 52 No 3 (2008), 727–744.

[11] K. -i. Kawasaki, On a category of cofinite modules which is Abelian, Mathematische Zeitschrift, 269 Issue 1 (2011), 587-608.

[12] J. Lipman, Lectures on Local cohomology and duality, Local cohomology and its applications, Lecture notes in pure and applied mathematics, Vol. 226, Marcel Dekker, Inc., New York·Basel, (2002), 39–89.

[13] E. Matlis, Injective Modules over noetherian rings, Pacific Journal of Mathematics, 8 (1958), 511–528.

[14] L. Melkersson, Modules cofinite with respect to an ideal, Journal of Algebra, 285 (2005), 649–668.

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