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An intersection multiplicity in terms of  -modules
Author(s):
C-Y.
Jean
Chan
Journal:
Proc. Amer. Math. Soc.
130
(2002),
327-336.
MSC (2000):
Primary 13D22, 13H15, 14C17, 13D07
Posted:
May 25, 2001
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Abstract:
The main aim of this paper is to discuss the relation between Serre's intersection multiplicity and the Euler form. The Euler form is defined to be an alternating sum of the length of  -modules and is used by Mori and Smith to develop intersection theory over noncommutative rings. We show that they differ by a sign and that this relation is closely related to Serre's vanishing theorem.
References:
-
- 1.
- H. BASS, On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8-28. MR 27:3669
- 2.
- S. P. DUTTA Generalized Intersection Multiplicities of Modules, Trans. Amer. Math. Soc., 276, no. 2, (1983), 657-669. MR 84i:13024
- 3.
- S. P. DUTTA Generalized Intersection Multiplicities of Modules II, Proc. Amer. Math. Soc., 93, no. 2, (1985), 203-204. MR 86k:13026
- 4.
- S. P. DUTTA, M. HOCHSTER AND J.E. MCLAUGHLIN, Modules of finite projective dimension with negative intersection multiplicities, Invent. Math. 79 (1985), 253-291. MR 86h:13023
- 5.
- W. FULTON Intersection Theory, Second edition, Springer-Verlag, Berlin, 1998. MR 99d:14003
- 6.
- H. GILLET AND C. SOUL´E, K-théorie et nullité des multiplicités d'intersection, C. R. Acad. Sci. Paris, Sér. I, no. 3, t. 300 (1985), 71-74. MR 86k:13027
- 7.
- H. MATSUMURA Commutative Ring Theory, Cambridge University Press, Cambridge, England, 1986. MR 88h:13001
- 8.
- I. MORI, Intersection multiplicity over noncommutative algebras, to appear in J. Algebra.
- 9.
- I. MORI AND S. P. SMITH, Bézout's theorem for noncommutative projective spaces, J. Pure Appl. Algebra 157 (2001), 279-299.
- 10.
- P. C. ROBERTS, Multiplicities and Chern Classes in Local Algebra, Cambridge Tracts in Mathematics 133, Cambridge University Press (1998). CMP 99:13
- 11.
- P. ROBERTS, The vanishing of intersection multiplicities of perfect complexes, Bull. Amer. Math. Soc. 13 (1985), 127-130. MR 87c:13030
- 12.
- P. ROBERTS, Intersection Theorems, Commutative Algebra, Proc. MSRI Microprogram, Springer-Verlag, 417-436. MR 90j:13024
- 13.
- P. ROBERTS, The MacRae Invariant and the First Local Chern Character, Trans. Amer. Math. Soc., 300, no. 2, (1987), 583-591. MR 88c:14010
- 14.
- P. ROBERTS, Local Chern Characters and Intersection Multiplicities, Proceedings of Symposia in Pure Mathematics, 46, (1987), 389-400. MR 89a:14011
- 15.
- J. ROTMAN, An Introduction to Homological Algebra Academic Press, New York, 1979. MR 80k:18001
- 16.
- J.-P. SERRE, Algèbre Locale-multiplicités, Lecture Notes in Mathematics 11, Springer-Verlag, New York, 1961. MR 34:1352
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Additional Information:
C-Y.
Jean
Chan
Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112
Address at time of publication:
Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, Indiana 47907-1395
Email:
cyjan@math.utah.edu
DOI:
10.1090/S0002-9939-01-06022-1
PII:
S 0002-9939(01)06022-1
Keywords:
Intersection multiplicity,
Chern character,
Euler characteristic,
Euler form
Received by editor(s):
October 11, 1999
Received by editor(s) in revised form:
June 15, 2000
Posted:
May 25, 2001
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
2001,
American Mathematical Society
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