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A Unified Approach to Local Cohomology Modules using Serre Classes

Published online by Cambridge University Press:  20 November 2018

Mohsen Asgharzadeh  and
Massoud Tousi
Mohsen Asgharzadeh
Affiliation:
Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran, and , School of Mathematics, Institute for Research in Fundamental Sciences(IPM), P.O. Box 19395-5746, Tehran, Iran e-mail: [email protected]@ipm.ir
Massoud Tousi
Affiliation:
Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran, and , School of Mathematics, Institute for Research in Fundamental Sciences(IPM), P.O. Box 19395-5746, Tehran, Iran e-mail: [email protected]@ipm.ir
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Abstract

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This paper discusses the connection between the local cohomology modules and the Serre classes of $R$-modules. This connection has provided a common language for expressing some results regarding the local cohomology $R$-modules that have appeared in different papers.

Keywords

13D45associated prime idealslocal cohomology modulesSerre class
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 4 , 01 December 2010 , pp. 577 - 586
Copyright
Copyright © Canadian Mathematical Society 2010

References

[AKS] Asadollahi, J., Khashyarmanesh, K., and Salaarian, S., On the finiteness properties of the generalized local cohomology modules. Comm. Alg. 30(2002), no. 2, 859–867. doi:10.1081/AGB-120013186Google Scholar
[ADT] Asgharzadeh, M., Divaani-Aazar, K., and Tousi, M., Finiteness dimension of local cohomology modules and its dual notion. J. Pure Appl. Algebra 213(2009), no. 3, 321–328. doi:10.1016/j.jpaa.2008.07.006Google Scholar
[BN] Bahmanpour, K. and Naghipour, R., On the cofiniteness of local cohohomology modules. Proc. Amer. Math. Soc. 136(2008), no. 7, 2359–2363. doi:10.1090/S0002-9939-08-09260-5Google Scholar
[BL] Brodmann, M. P., Faghani, A., and Lashgari, A., A finiteness result for associated primes of local cohomology modules. Proc. Amer. Math. Soc. 128(2000), no. 10, 2851–2853. doi:10.1090/S0002-9939-00-05328-4Google Scholar
[BS] Brodmann, M. P. and Sharp, R. Y., Local cohomology: an algebraic introduction with geometric applications. Cambridge Studies in Advanced Mathematics, 60, Cambridge University Press, Cambridge, 1998.Google Scholar
[DM] Divaani-Aazar, K. and Mafi, A., Associated prime of local cohomology modules. Proc. Amer. Math. Soc. 133(2005), no. 3, 655–660. doi:10.1090/S0002-9939-04-07728-7Google Scholar
[DNT] Divaani-Aazar, K., Naghipour, R., and Tousi, M., Cohomological dimension of certain algebraic varieties. Proc. Amer. Math. Soc. 130(2002), no. 12, 3537–3544. doi:10.1090/S0002-9939-02-06500-0Google Scholar
[DY] Dibaei, M. T. and Yassemi, S., Associated primes and cofiniteness of local cohomology modules. Manuscripta Math. 117(2005), no. 2, 199–205. doi:10.1007/s00229-005-0538-5Google Scholar
[Har1] Hartshorne, R., Cohomological dimension of algebraic varieties. Ann. of Math. 88(1968), 403–450. doi:10.2307/1970720Google Scholar
[Har2] Hartshorne, R., Affine duality and cofiniteness. Invent. Math. 9(1969/1970), 145–164. doi:10.1007/BF01404554Google Scholar
[Hel] Hellus, M., A note on the injective dimension of local cohomology modules. Proc. Amer. Math. Soc. 136(2008), no. 7, 2313–2321. doi:10.1090/S0002-9939-08-09198-3Google Scholar
[HS] Huneke, C. L. and Sharp, R. Y., Bass numbers of local cohomology modules. Trans. Amer. Math. Soc. 339(1993), no. 2, 765–779. doi:10.2307/2154297Google Scholar
[Hu] Huneke, C. L., Problems on local cohomology. In: Free resolutions in commutative algebra and algebraic geometry (Sundance, Utah, 1990), Research Notes in Mathematics, 2, Jones and Bartlett, Boston, MA, 1994, pp. 93–108.Google Scholar
[KS] Khashyarmanesh, K. and Salaarian, S., On the associated primes of local cohomology modules. Comm. Alg. 27(1999), no. 12, 6191–6198. doi:10.1080/00927879908826816Google Scholar
[LSY] Lorestani, K. B., Sahandi, P., and Yassemi, S., Artinian local cohomology modules. Canad. Math. Bull. 50(2007), no. 4, 598–602.Google Scholar
[L1] Lyubeznik, G., Finiteness properties of local cohomology modules (an application of D-modules to commutative algebra). Invent. Math. 113(1993), no. 1, 41–55. doi:10.1007/BF01244301Google Scholar
[L2] Lyubeznik, G., Finiteness properties of local cohomology modules for regular local rings of mixed characteristic: the unramified case. Comm. Algebra 28(2000), no. 12, 5867–5882. doi:10.1080/00927870008827193Google Scholar
[M] Melkersson, L., Modules cofinite with respect to an ideal. J. Algebra 285(2005), no. 2, 649–668. doi:10.1016/j.jalgebra.2004.08.037Google Scholar
[MV] Marley, T. and Vassilev, J. C., Local cohomology modules with infinite dimensional socles. Proc. Amer. Math. Soc. 132(2004), no. 12, 3485–3490. doi:10.1090/S0002-9939-04-07658-0Google Scholar
[R] Rudlof, P., On minimax and related modules. Canada J. Math. 44(1992), no. 1, 154–166.Google Scholar
[V] Vasconcelos, W. V., Divisor theory in module categories, North-Holland Mathematics Studies, 14, Notas de Matemática, 53, North-Holland Publishing Co., Amsterdam-Oxford, 1974.Google Scholar
[Z] Zochinger, H., Minimax modules. J. Algebra 102(1986), no. 1, 1–32. doi:10.1016/0021-8693(86)90125-0Google Scholar