Faltings’ theorem for the annihilation of local cohomology modules over a Gorenstein ring
HTML articles powered by AMS MathViewer
- by K. Khashyarmanesh and Sh. Salarian PDF
- Proc. Amer. Math. Soc. 132 (2004), 2215-2220 Request permission
Abstract:
In this paper we study the Annihilator Theorem and the Local-global Principle for the annihilation of local cohomology modules over a (not necessarily finite-dimensional) Noetherian Gorenstein ring.References
- Markus Brodmann, Einige Ergebnisse aus der lokalen Kohomologietheorie und ihre Anwendung, Osnabrücker Schriften zur Mathematik. Reihe M: Mathematische Manuskripte [Osnabrück Publications in Mathematics. Series M: Mathematical Manuscripts], vol. 5, Universität Osnabrück, Fachbereich Mathematik, Osnabrück, 1983 (German). MR 838084
- M. Brodmann, Ch. Rotthaus, and R. Y. Sharp, On annihilators and associated primes of local cohomology modules, J. Pure Appl. Algebra 153 (2000), no. 3, 197–227. MR 1783166, DOI 10.1016/S0022-4049(99)00104-8
- M. P. Brodmann and R. Y. Sharp, Local cohomology: an algebraic introduction with geometric applications, Cambridge Studies in Advanced Mathematics, vol. 60, Cambridge University Press, Cambridge, 1998. MR 1613627, DOI 10.1017/CBO9780511629204
- Lars Winther Christensen, Gorenstein dimensions, Lecture Notes in Mathematics, vol. 1747, Springer-Verlag, Berlin, 2000. MR 1799866, DOI 10.1007/BFb0103980
- Gerd Faltings, Über die Annulatoren lokaler Kohomologiegruppen, Arch. Math. (Basel) 30 (1978), no. 5, 473–476 (German). MR 506246, DOI 10.1007/BF01226087
- Gerd Faltings, Der Endlichkeitssatz in der lokalen Kohomologie, Math. Ann. 255 (1981), no. 1, 45–56 (German). MR 611272, DOI 10.1007/BF01450555
- K. N. Raghavan, Local-global principle for annihilation of local cohomology, Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992) Contemp. Math., vol. 159, Amer. Math. Soc., Providence, RI, 1994, pp. 329–331. MR 1266189, DOI 10.1090/conm/159/01513
- K. Raghavan, Uniform annihilation of local cohomology and of Koszul homology, Math. Proc. Cambridge Philos. Soc. 112 (1992), no. 3, 487–494. MR 1177997, DOI 10.1017/S0305004100071164
Additional Information
- K. Khashyarmanesh
- Affiliation: Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran – and – Department of Mathematics, Damghan University, P.O. Box 36715-364, Damghan, Iran
- Email: Khashyar@ipm.ir
- Sh. Salarian
- Affiliation: Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran – and – Department of Mathematics, Damghan University, P.O. Box 36715-364, Damghan, Iran
- Email: Salarian@ipm.ir
- Received by editor(s): June 5, 2002
- Received by editor(s) in revised form: March 5, 2003
- Published electronically: March 10, 2004
- Additional Notes: This research was in part supported by a grant from IPM (No. 81130021 and No. 81130117).
- Communicated by: Bernd Ulrich
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2215-2220
- MSC (2000): Primary 13D45, 13E05, 13H10, 13D05, 13C15
- DOI: https://doi.org/10.1090/S0002-9939-04-07322-8
- MathSciNet review: 2052396