References
[A1] Auslander, M.: Modules over unramified regular local rings. Illinois J. Math.5, 631–645 (1961)
[A2] Auslander, M.: Modules over unramified regular local rings. Proc. Intern. Congress of Math. 1962, pp. 230–233
[D1] Dutta, S.P.: Generalized intersection multiplicities of modules. Trans. Amer. Math. Soc.276, 657–669 (1983)
[D2] Dutta, S.P.: Weak linking and multiplicities. J. Pure and Applied Algebra27, 111–130 (1983)
[D3] Dutta, S.P.: Symbolic powers, intersection multiplielty, and asymptotic behavior of Tor. J. London Math. Soc. (2)28, 261–281 (1983)
[D4] Dutta, S.P.: Frobenius and multiplicities. J. of Algebra85, 424–448 (1983)
[D5] Dutta, S.P.: Generalized intersection multiplicities of modules II. Proc. A.M.S. (in press) (1984)
[DHM] Dutta, S.B., Hochster, M., McLaughlin, I.E.: Appendix to “Modules of Finite Projective Dimension with Negative Intersection Multiplicities,” manuscript available from the authors
[E] Eisenbud, D.: Homological algebra on a local complete intersection, with an application to group representations. Trans. Amer. Math. Soc.260, 35–64 (1980)
[F1] Fossum, R.:æ-theory. Preprint Series, Politecnico di Torino, 1977
[F2] Fossum. R.: Correspondence, 1983
[FFI] Fossum, R., Foxby, H.-B., Iversen, B.: Characteristic classes of complexes. Preliminary preprint
[H1] Hochster, M.: Cohen-Macaulay modules. Conference on Commutative Algebra. Lecture Notes in Math. Vol. 311, pp. 120–152. Berlin-Heidelberg-New York Springer 1973
[H2] Hochster, M.: Topics in the homological theory of modules over commutative rings, C.B.M.S. Regional Conference Series in Math., Vol. 24. Amer. Math. Soc., Providence, R.I., 1975
[H3] Hochster, M.: The local homological conjectures. In: Commutative Algebra: Durham 1981. Cambridge Univ. Press, London Math. Soc. Lecture Note Series. Vol. 72, pp. 32–54 (1982)
[H4] Hochster, M.: Euler characteristics over unramified regular local rings. Illinois J. Math. in press (1984)
[L] Lichtenbaum, S.: On the vanishing of Tor in regular local rings. Illinois J. Math.10, 220–226 (1966)
[M] Malliavin-Brameret, M.-P.: Une remarque sur les anneaux locaux réguliers, Sém. Dubreil-Pisot (Algèbre et Théorie des Nombres), 24 année, 1970/71, no 13
[PS1] Peskine, C., Szpiro, L.: Dimension projective finie et cohomologie locale. Inst. Hautes Etudes Sci. Publ. Math.42, 323–395 (1973)
[PS2] Peskine, C., Szpiro, L.: Syzygies et multiplicités. C.R. Acad. Sci. Paris Ser. A-B278, 1421–1424 (1974)
[S] Serre, J.P.: Algèbre locale. Multiplicités. Lecture Notes in Math. Vol. 11, 3éme édition. Berlin-Heidelberg-New York: Springer 1975
[W] Weil, A.: Foundations of algebraic geometry. Amer. Math. Soc. Colloq. Publ. Vol. 29, Amer. Math. Soc., Providence, R.I., Revised ed., 1962
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Dutta, S.P., Hochster, M. & McLaughlin, J.E. Modules of finite projective dimension with negative intersection multiplicities. Invent Math 79, 253–291 (1985). https://doi.org/10.1007/BF01388973
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DOI: https://doi.org/10.1007/BF01388973