Bulletin of the American Mathematical Society

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Book Information:

Author: Paul C. Roberts
Title: Multiplicities and Chern classes in local algebra
Additional book information: Cambridge Tracts in Mathematics, vol. 133, Cambridge University Press, Cambridge, 1998, xi+303 pp., ISBN 0-521-47316-0, $59.95$

[Aus]

M. Auslander, Modules over unramified regular local rings, Proc. International Congress of Mathematics in Stockholm 1962, Uppsala, Almqvist and Wiksells (1963), 230-234. MR 0175930

[Bass]

H. Bass, On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8-28. MR 0153708

[BFM]

P. Baum, W. Fulton, and R. MacPherson, Riemann-Roch for singular varieties, Publ. Math. I.H.E.S. 45 (1975), 101-145. MR 0412190

[Ber]

P. Berthelot, Altération de variétés algébriques [d'après de Jong], Séminaire Bourbaki n. 815 (1996). MR 1472543

[Bou]

J.-F. Boutot, Singularités rationnelles et quotients par les groupes réductifs, Invent. Math. 88 (1987), 65-68. MR 0877006

[Bru]

W. Bruns, Tight closure, Bull. Amer. Math. Soc. 33 (1996), 447-458. MR 1397097

[BruH]

W. Bruns and J. Herzog, Cohen-Macaulay Rings, vol. 39, Cambridge studies in advanced mathematics, 1993. MR 1251956

[DeJ]

A. de Jong, Smoothness, semi-stability, and alterations, Publ. Math. I.H.E.S. 83 (1996), 51-93. MR 1423020

[Du1]

S. P. Dutta, Frobenius and multiplicities, J. Algebra 85 (1983), 424-448. MR 0725094

[Du2]

-, On the canonical element conjecture, Trans. Amer. Math. Soc. 299 (1987), 803-811. MR 0869233

[DHM]

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 0778127

[EvG]

E. G. Evans and P. Griffith, The syzygy problem, Annals of Math. 114 (1981), 323-333. MR 0632842

[F]

W. Fulton, Intersection Theory, Springer-Verlag, Berlin, 1984. MR 0732620

[FM]

W. Fulton and R. MacPherson, Categorical framework for the study of singular spaces, Mem. Amer. Math. Soc. 31, 1981. MR 0609831

[GS]

H. Gillet and C. Soulé, K-théorie et nullité des multiplicités d'intersection, C. R. Acad. Sci. Paris Série I no. 3 t. 300 (1985), 71-74. MR 0777736

[HaMo]

C. Han and P. Monsky, Some surprising Hilbert-Kunz functions, Math. Z. 214 (1993), 119-135. MR 1234602

[Heit]

R. Heitmann, A counterexample to the rigidity conjecture for rings, Bull. Amer. Math. Soc. New Series 29 (1993), 94-97. MR 1197425

[Ho1]

M. Hochster, Contracted ideals from integral extensions of regular rings, Nagoya Math. J. 51 (1973), 25-43. MR 0349656

[Ho2]

-, Topics in the homological theory of modules over commutative rings, C.B.M.S. Regional Conf. Ser. in Math. No. 24, Amer. Math. Soc., Providence, R.I., 1975. MR 0371879

[Ho3]

-, Canonical elements in local cohomology modules and the direct summand conjecture, J. of Algebra 84 (1983), 503-553. MR 0723406

[HH1]

-, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31-116. MR 1017784

[HH2]

-, Infinite integral extensions and big Cohen-Macaulay algebras, Annals of Math. 135 (1992), 53-89. MR 1147957

[HH3]

-, Applications of the existence of big Cohen-Macaulay algebras, Advances in Math. 113 (1995), 45-117. MR 1332808

[HR]

M. Hochster and J. L. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Advances in Math. 13 (1974), 115-175. MR 0347810

[Hu]

C. Huneke, Tight Closure and Its Applications, Proc. of the CBMS Conference held at Fargo, North Dakota, July, 1995, C.B.M.S. Regional Conference Series, Amer. Math. Soc., Providence, R.I., 1996. MR 1377268

[PS1]

C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale, Publ. Math. I.H.E.S. (Paris) 42 (1973), 323-395. MR 0374130

[PS2]

-, Syzygies et multiplicités, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1421-1424. MR 0349659

[Rang]

N. Ranganathan, Splitting in module-finite extension rings and the vanishing conjecture for maps of Tor, Thesis, University of Michigan, expected 2000.

[Ro1]

P. Roberts, Two applications of dualizing complexes over local rings, Ann. Sci. Ec. Norm. Sup. 9 (1976), 103-106. MR 0399075

[Ro2]

-, Cohen-Macaulay complexes and an analytic proof of the new intersection conjecture, J. of Algebra 66 (1980), 225-230. MR 0591254

[Ro3]

-, The vanishing of intersection multiplicities of perfect complexes, Bull. Amer. Math. Soc. 13 (1985), 127-130. MR 0799793

[Ro4]

-, Le théorème d'intersection, C. R. Acad. Sc. Paris Sér. I 304 (1987), 177-180. MR 0880574

[Ro5]

-, Intersection theorems, in Commutative Algebra, Math. Sci. Research Inst. Publ. 15, Springer-Verlag, New York-Berlin-Heidelberg, 1989, pp. 417-436. MR 1015532

[Se]

J.-P. Serre, Algèbre locale. Multiplicités, Lecture Notes in Mathematics 11, Springer-Verlag, New York, 1965. MR 0201468

[Aus]

M. Auslander, Modules over unramified regular local rings, Proc. International Congress of Mathematics in Stockholm 1962, Uppsala, Almqvist and Wiksells (1963), 230-234. MR 0175930

[Bass]

H. Bass, On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8-28. MR 0153708

[BFM]

P. Baum, W. Fulton, and R. MacPherson, Riemann-Roch for singular varieties, Publ. Math. I.H.E.S. 45 (1975), 101-145. MR 0412190

[Ber]

P. Berthelot, Altération de variétés algébriques [d'après de Jong], Séminaire Bourbaki n. 815 (1996). MR 1472543

[Bou]

J.-F. Boutot, Singularités rationnelles et quotients par les groupes réductifs, Invent. Math. 88 (1987), 65-68. MR 0877006

[Bru]

W. Bruns, Tight closure, Bull. Amer. Math. Soc. 33 (1996), 447-458. MR 1397097

[BruH]

W. Bruns and J. Herzog, Cohen-Macaulay Rings, vol. 39, Cambridge studies in advanced mathematics, 1993. MR 1251956

[DeJ]

A. de Jong, Smoothness, semi-stability, and alterations, Publ. Math. I.H.E.S. 83 (1996), 51-93. MR 1423020

[Du1]

S. P. Dutta, Frobenius and multiplicities, J. Algebra 85 (1983), 424-448. MR 0725094

[Du2]

-, On the canonical element conjecture, Trans. Amer. Math. Soc. 299 (1987), 803-811. MR 0869233

[DHM]

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 0778127

[EvG]

E. G. Evans and P. Griffith, The syzygy problem, Annals of Math. 114 (1981), 323-333. MR 0632842

[F]

W. Fulton, Intersection Theory, Springer-Verlag, Berlin, 1984. MR 0732620

[FM]

W. Fulton and R. MacPherson, Categorical framework for the study of singular spaces, Mem. Amer. Math. Soc. 31, 1981. MR 0609831

[GS]

H. Gillet and C. Soulé, K-théorie et nullité des multiplicités d'intersection, C. R. Acad. Sci. Paris Série I no. 3 t. 300 (1985), 71-74. MR 0777736

[HaMo]

C. Han and P. Monsky, Some surprising Hilbert-Kunz functions, Math. Z. 214 (1993), 119-135. MR 1234602

[Heit]

R. Heitmann, A counterexample to the rigidity conjecture for rings, Bull. Amer. Math. Soc. New Series 29 (1993), 94-97. MR 1197425

[Ho1]

M. Hochster, Contracted ideals from integral extensions of regular rings, Nagoya Math. J. 51 (1973), 25-43. MR 0349656

[Ho2]

-, Topics in the homological theory of modules over commutative rings, C.B.M.S. Regional Conf. Ser. in Math. No. 24, Amer. Math. Soc., Providence, R.I., 1975. MR 0371879

[Ho3]

-, Canonical elements in local cohomology modules and the direct summand conjecture, J. of Algebra 84 (1983), 503-553. MR 0723406

[HH1]

-, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31-116. MR 1017784

[HH2]

-, Infinite integral extensions and big Cohen-Macaulay algebras, Annals of Math. 135 (1992), 53-89. MR 1147957

[HH3]

-, Applications of the existence of big Cohen-Macaulay algebras, Advances in Math. 113 (1995), 45-117. MR 1332808

[HR]

M. Hochster and J. L. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Advances in Math. 13 (1974), 115-175. MR 0347810

[Hu]

C. Huneke, Tight Closure and Its Applications, Proc. of the CBMS Conference held at Fargo, North Dakota, July, 1995, C.B.M.S. Regional Conference Series, Amer. Math. Soc., Providence, R.I., 1996. MR 1377268

[PS1]

C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale, Publ. Math. I.H.E.S. (Paris) 42 (1973), 323-395. MR 0374130

[PS2]

-, Syzygies et multiplicités, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1421-1424. MR 0349659

[Rang]

N. Ranganathan, Splitting in module-finite extension rings and the vanishing conjecture for maps of Tor, Thesis, University of Michigan, expected 2000.

[Ro1]

P. Roberts, Two applications of dualizing complexes over local rings, Ann. Sci. Ec. Norm. Sup. 9 (1976), 103-106. MR 0399075

[Ro2]

-, Cohen-Macaulay complexes and an analytic proof of the new intersection conjecture, J. of Algebra 66 (1980), 225-230. MR 0591254

[Ro3]

-, The vanishing of intersection multiplicities of perfect complexes, Bull. Amer. Math. Soc. 13 (1985), 127-130. MR 0799793

[Ro4]

-, Le théorème d'intersection, C. R. Acad. Sc. Paris Sér. I 304 (1987), 177-180. MR 0880574

[Ro5]

-, Intersection theorems, in Commutative Algebra, Math. Sci. Research Inst. Publ. 15, Springer-Verlag, New York-Berlin-Heidelberg, 1989, pp. 417-436. MR 1015532

[Se]

J.-P. Serre, Algèbre locale. Multiplicités, Lecture Notes in Mathematics 11, Springer-Verlag, New York, 1965. MR 0201468