The category of cofinite modules for ideals of dimension one and codimension one
Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 123-126.
Publié le :
DOI : 10.5802/acirm.48
Classification : 14B15, 13D03, 18G15
Mots clés : Abelian category, Derived category, Cofinite complex, Cofinite module
Kawasaki, Ken-ichiroh 1

1 Department of Mathematics, Nara University of Education, Takabatake-cho, Nara, 630-8528, Japan
@article{ACIRM_2010__2_2_123_0,
     author = {Kawasaki, Ken-ichiroh},
     title = {The category of cofinite modules for ideals of dimension one and codimension one},
     journal = {Actes des rencontres du CIRM},
     pages = {123--126},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     doi = {10.5802/acirm.48},
     zbl = {1439.14025},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/acirm.48/}
}
TY  - JOUR
AU  - Kawasaki, Ken-ichiroh
TI  - The category of cofinite modules for ideals of dimension one and codimension one
JO  - Actes des rencontres du CIRM
PY  - 2010
SP  - 123
EP  - 126
VL  - 2
IS  - 2
PB  - CIRM
UR  - http://www.numdam.org/articles/10.5802/acirm.48/
DO  - 10.5802/acirm.48
LA  - en
ID  - ACIRM_2010__2_2_123_0
ER  - 
%0 Journal Article
%A Kawasaki, Ken-ichiroh
%T The category of cofinite modules for ideals of dimension one and codimension one
%J Actes des rencontres du CIRM
%D 2010
%P 123-126
%V 2
%N 2
%I CIRM
%U http://www.numdam.org/articles/10.5802/acirm.48/
%R 10.5802/acirm.48
%G en
%F 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, Tome 2 (2010) no. 2, pp. 123-126. doi : 10.5802/acirm.48. http://www.numdam.org/articles/10.5802/acirm.48/

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

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

[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). | Zbl

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

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

[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. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

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

[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. | Zbl

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

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

Cité par Sources :