Abstract
The “intersections” referred to in the title of this paper are intersections of the kind which came into Commutative Algebra from Intersection Theory in Algebraic Geometry, and the “theorems” are descendants of the Intersection Theorem of Peskine and Szpiro [15,16]. There are other kinds of theorems which go under this name, notably Krull’s Intersection Theorem on the intersection of the powers of an ideal; we will not be discussing these here.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
P. Baum, W. Fulton and R. MacPherson, Riemann-Roch for singular varieties, Publ. Math. IHES 45 (1975), 101–145.
S. P. Dutta, Frobenius and Multiplicities, J. of Algebra 85 (1983), 424–448.
S. P. Dutta, Generalized intersection multiplicities of modules II, Proc. Amer. Math. Soc. 93 (1985), 203–204.
S. P. Dutta, On the canonical element conjecture, Trans. Amer. Math. Soc. 299 (1987), 803–811.
S. P. Dutta, M. Höchster, and J. E. McLaughlin, Modules of finite projective dimen¬sion with negative intersection multiplicities, Invent. Math. 79 (1985), 253–291.
E. G. Evans and P. Griffith, The syzygy problem, Ann. of Math. 114 (1981), 323–333.
E. G. Evans and P. Griffith, The syzygy problem: a new proof and historical perspective, in “Commutative Algebra,” (Durham 1981), London Math Soc. Lecture Note Series, vol. 72, 1982, pp. 2–11.
H.-B. Foxby, The MacRae invariant, in “Commutative Algebra,” (Durham 1981), London Math Soc. Lecture Note Series, vol. 72, 1982, pp. 121–128.
W. Fulton, “Intersection Theory,” Springer-Verlag, Berlin, 1984.
M. Höchster, The equicharacteristic case of some homological conjectures on local rings, Bull. Amer. Math. Soc. 80 (1974), 683–686.
M. Höchster, “Topics in the homological theory of modules over commutative rings,” Regional Conference Series in Mathematics, vol. 24, 1975.
M. Höchster, Canonical elements in local cohomology modules and the direct summand conjecture, Journal of Algebra 84 (1983), 503–553.
B. Iversen, Local Chern classes, Ann. Scient. Éc. Norm. Sup. 9 (1976), 155–169.
R. E. MacRae, On an application of the Fitting invariants, J. of Algebra 2 (1965), 153–169.
C. Peskine and L. Szpiro, Sur la topologie des sous-schémas fermés d’un schéma localement noethérien, définis comme support d’un faisceau cohérent localement de dimension projective finie, C. R. Acad. Sci. Paris Sér. A 269 (1969), 49–51.
C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale, Publ. Math. IHES 42 (1973), 47–119.
C. Peskine and L. Szpiro, Syzygies et Multiplicités, C. R. Acad. Sci. Paris Sr. A 278 (1974), 1421–1424.
P. Roberts, Two applications of dualizing complexes over local rings, Ann. Sci. Ec. Norm. Sup. 9 (1976), 103–106.
P. Roberts, The vanishing of intersection multiplicities of perfect complexes, Bull. Amer. Math. Soc. 13 (1985), 127–130.
P. Roberts, The MacRae invariant and the first local Chern character,, Trans. Amer. Math. Soc. 300 (1987), 583–591.
P. Roberts, Le théorème d’intersection, C. R. Acad. Se. Paris Sér. I no. 7, 304 (1987), 177–180.
G. Seibert, Complexes with homology of finite length and Frobenius functors, to appear.
L. Szpiro, Sur la théorie des complexes parfaits, in “Commutative Algebra,” (Durham 1981), London Math Soc. Lecture Note Series, vol. 72, 1982, pp. 83–90.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag New York Inc.
About this paper
Cite this paper
Roberts, P. (1989). Intersection Theorems. In: Hochster, M., Huneke, C., Sally, J.D. (eds) Commutative Algebra. Mathematical Sciences Research Institute Publications, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3660-3_23
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3660-3_23
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8196-2
Online ISBN: 978-1-4612-3660-3
eBook Packages: Springer Book Archive