The Michigan Mathematical Journal

The Chern coefficients of local rings

Wolmer Vasconcelos

Source: Michigan Math. J. Volume 57 (2008), 725-743.

Primary Subjects: 13A30
Secondary Subjects: 13B22, 13H10, 13H15

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.mmj/1220879434
Digital Object Identifier: doi:10.1307/mmj/1220879434
Mathematical Reviews number (MathSciNet): MR2492478

References

I. M. Aberbach and C. Huneke, An improved Briançon--Skoda theorem with applications to the Cohen--Macaulayness of Rees algebras, Math. Ann. 297 (1993), 343--369.
Mathematical Reviews (MathSciNet): MR1241812
Digital Object Identifier: doi:10.1007/BF01459507
M. Auslander and D. Buchsbaum, On ramification theory in noetherian rings, Amer. J. Math. 81 (1959), 749--765.
Mathematical Reviews (MathSciNet): MR106929
Digital Object Identifier: doi:10.2307/2372926
W. Bruns and J. Herzog, Cohen--Macaulay rings, Cambridge Stud. Adv. Math., 39, Cambridge Univ. Press, Cambridge, 1993.
Mathematical Reviews (MathSciNet): MR1251956
Zentralblatt MATH: 0788.13005
L. Burch, Codimension and analytic spread, Math. Proc. Cambridge Philos. Soc. 72 (1972), 369--373.
Mathematical Reviews (MathSciNet): MR304377
Digital Object Identifier: doi:10.1017/S0305004100047198
A. Corso, Sally modules of $\text\frak m$-primary ideals in local rings, preprint, 2003.
K. Dalili and W. V. Vasconcelos, The tracking number of an algebra, Amer. J. Math. 127 (2005), 697--708.
Mathematical Reviews (MathSciNet): MR2141649
Zentralblatt MATH: 02211502
Digital Object Identifier: doi:10.1353/ajm.2005.0019
L. R. Doering, T. Gunston, and W. V. Vasconcelos, Cohomological degrees and Hilbert functions of graded modules, Amer. J. Math. 120 (1998), 493--504.
Mathematical Reviews (MathSciNet): MR1623400
Zentralblatt MATH: 0924.13011
Digital Object Identifier: doi:10.1353/ajm.1998.0019
J. Elias, Upper bounds of Hilbert coefficients and Hilbert functions, Math. Proc. Cambridge Philos. Soc. (to appear).
Mathematical Reviews (MathSciNet): MR2431640
Digital Object Identifier: doi:10.1017/S0305004108001138
G. Evans and P. Griffith, Local cohomology modules for normal domains, J. London Math. Soc. (2) 19 (1979), 277--284.
Mathematical Reviews (MathSciNet): MR533326
Digital Object Identifier: doi:10.1112/jlms/s2-19.2.277
S. Goto and K. Nishida, Hilbert coefficients and Buchsbaumness of associated graded rings, J. Pure Appl. Algebra 181 (2003), 61--74.
Mathematical Reviews (MathSciNet): MR1971805
Digital Object Identifier: doi:10.1016/S0022-4049(02)00325-0
P. Griffith, A representation theorem for complete local rings, J. Pure Appl. Algebra 7 (1976), 303--315.
Mathematical Reviews (MathSciNet): MR412176
Digital Object Identifier: doi:10.1016/0022-4049(76)90056-6
------, Maximal Cohen--Macaulay modules and representation theory, J. Pure Appl. Algebra 13 (1978), 321--334.
Mathematical Reviews (MathSciNet): MR509166
Digital Object Identifier: doi:10.1016/0022-4049(78)90013-0
T. Gunston, Cohomological degrees, Dilworth numbers and linear resolution, Ph.D. thesis, Rutgers Univ., 1998.
J. Herzog, A. Simis, and W. V. Vasconcelos, Approximation complexes of blowing-up rings, J. Algebra 74 (1982), 466--493.
Mathematical Reviews (MathSciNet): MR647249
Digital Object Identifier: doi:10.1016/0021-8693(82)90034-5
M. Hochster, Presentation depth and the Lipman--Sathaye Jacobian theorem, The Roos festschrift, vol. 2, Homology Homotopy Appl. 4 (2002), 295--314.
Mathematical Reviews (MathSciNet): MR1918514
Project Euclid: euclid.hha/1139852467
M. Hochster and C. Huneke, Tight closure in equal characteristic zero, preprint.
Mathematical Reviews (MathSciNet): MR1015524
C. Huneke, On the associated graded ring of an ideal, Illinois J. Math. 26 (1982), 121--137.
Mathematical Reviews (MathSciNet): MR638557
C. Huneke and B. Ulrich, General hyperplane sections of algebraic varieties, J. Algebraic Geom. 2 (1993), 487--505.
Mathematical Reviews (MathSciNet): MR1211996
C. H. Linh, Upper bound for the Castelnuovo--Mumford regularity of associated graded modules, Comm. Algebra 33 (2005), 1817--1831.
Mathematical Reviews (MathSciNet): MR2150846
Digital Object Identifier: doi:10.1081/AGB-200063340
J. Lipman and A. Sathaye, Jacobian ideals and a theorem of Briançon--Skoda, Michigan Math. J. 28 (1981), 199--222.
Mathematical Reviews (MathSciNet): MR616270
Digital Object Identifier: doi:10.1307/mmj/1029002510
Project Euclid: euclid.mmj/1029002510
M. Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, 13, Interscience, New York, 1962.
Mathematical Reviews (MathSciNet): MR155856
Zentralblatt MATH: 0123.03402
M. Narita, A note on the coefficients of Hilbert characteristic functions in semi-regular local rings, Math. Proc. Cambridge Philos. Soc. 59 (1963), 269--275.
Mathematical Reviews (MathSciNet): MR146212
Digital Object Identifier: doi:10.1017/S0305004100036884
E. Noether, Idealdifferentiation und Differente, J. Reine Angew. Math. 188 (1950), 1--21.
Mathematical Reviews (MathSciNet): MR38337
D. G. Northcott, A note on the coefficients of the abstract Hilbert function, J. London Math. Soc. 35 (1960), 209--214.
Mathematical Reviews (MathSciNet): MR110731
Digital Object Identifier: doi:10.1112/jlms/s1-35.2.209
T. Pham and W. V. Vasconcelos, Complexity of the normalization of algebras, Math. Z. 258 (2008), 729--743.
Mathematical Reviews (MathSciNet): MR2369053
Digital Object Identifier: doi:10.1007/s00209-007-0194-4
C. Polini, B. Ulrich, and W. V. Vasconcelos, Normalization of ideals and Briançon--Skoda numbers, Math. Res. Lett. 12 (2005), 827--842.
Mathematical Reviews (MathSciNet): MR2189243
D. Rees, Reductions of modules, Math. Proc. Cambridge Philos. Soc. 101 (1987), 431--449.
Mathematical Reviews (MathSciNet): MR878892
Digital Object Identifier: doi:10.1017/S0305004100066810
M. E. Rossi and G. Valla, The Hilbert function of the Ratliff--Rush filtration, J. Pure Appl. Algebra 201 (2005), 25--41.
Mathematical Reviews (MathSciNet): MR2158745
Digital Object Identifier: doi:10.1016/j.jpaa.2004.12.042
------, Hilbert function of filtered modules, preprint, arXiv:0710.2346.
R. Y. Sharp, Cohen--Macaulay properties for balanced big Cohen--Macaulay modules, Math. Proc. Cambridge Philos. Soc. 90 (1981), 229--238.
Mathematical Reviews (MathSciNet): MR620732
Digital Object Identifier: doi:10.1017/S0305004100058680
J. Stückrad and W. Vogel, Buchsbaum rings and applications, Springer-Verlag, Berlin, 1986.
Mathematical Reviews (MathSciNet): MR881220
G. Valla, Problems and results on Hilbert functions of graded algebras, Six lectures on commutative algebra (Bellaterra, 1996), Progr. Math., 166, pp. 293--344, Birkhäuser, Basel, 1998.
Mathematical Reviews (MathSciNet): MR1648668
Zentralblatt MATH: 0946.13012
W. V. Vasconcelos, The homological degree of a module, Trans. Amer. Math. Soc. 350 (1998), 1167--1179.
Mathematical Reviews (MathSciNet): MR1458335
Digital Object Identifier: doi:10.1090/S0002-9947-98-02127-8
------, Integral closure, Springer Monogr. Math., Springer-Verlag, Berlin, 2005.
Mathematical Reviews (MathSciNet): MR2153889

2009 © The University of Michigan