Tight closure, invariant theory, and the Briançon-Skoda theorem

Hochster, Melvin ; Huneke, Craig

Journal of the American Mathematical Society, Tome 03 (1990) no. 1, pp. 31-116

Détail

DOI : 10.1090/S0894-0347-1990-1017784-6

Bibliographie

[1] Artin, M. Algebraic approximation of structures over complete local rings Inst. Hautes Études Sci. Publ. Math. 1969 23 58

[2] Auslander, Maurice, Bridger, Mark Stable module theory 1969 146

[3] Boutot, Jean-Franã§Ois Singularités rationnelles et quotients par les groupes réductifs Invent. Math. 1987 65 68

[4] Buchsbaum, David A., Eisenbud, David What makes a complex exact? J. Algebra 1973 259 268

[5] Borel, Armand Linear algebraic groups 1969

[6] Skoda, Henri, Brianã§On, Joã«L Sur la clôture intégrale d’un idéal de germes de fonctions holomorphes en un point de 𝐶ⁿ C. R. Acad. Sci. Paris Sér. A 1974 949 951

[7] Bruns, Winfried, Vetter, Udo Determinantal rings 1988

[8] De Concini, Corrado, Eisenbud, David, Procesi, Claudio Hodge algebras 1982 87

[9] Dutta, Sankar P. Frobenius and multiplicities J. Algebra 1983 424 448

[10] Dutta, Sankar P. On the canonical element conjecture Trans. Amer. Math. Soc. 1987 803 811

[11] Dutta, S. P. Ext and Frobenius J. Algebra 1989 163 177

[12] Eagon, John A., Hochster, M. 𝑅-sequences and indeterminates Quart. J. Math. Oxford Ser. (2) 1974 61 71

[13] Eisenbud, David Homological algebra on a complete intersection, with an application to group representations Trans. Amer. Math. Soc. 1980 35 64

[14] Evans, E. Graham, Griffith, Phillip The syzygy problem Ann. of Math. (2) 1981 323 333

[15] Evans, E. Graham, Jr., Griffith, Phillip A. Order ideals 1989 213 225

[16] Fedder, Richard, Watanabe, Keiichi A characterization of 𝐹-regularity in terms of 𝐹-purity 1989 227 245

[17] Fulton, William Intersection theory 1984

[18] Grauert, Hans, Riemenschneider, Oswald Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen Invent. Math. 1970 263 292

[19] Hartshorne, Robin Local cohomology 1967

[20] Herzog, Jã¼Rgen Ringe der Charakteristik 𝑝 und Frobeniusfunktoren Math. Z. 1974 67 78

[21] Hochster, Melvin, Huneke, Craig Tightly closed ideals Bull. Amer. Math. Soc. (N.S.) 1988 45 48

[22] Hochster, Melvin, Huneke, Craig Tight closure 1989 305 324

[23] Hochster, Melvin, Huneke, Craig Tight closure and strong 𝐹-regularity Mém. Soc. Math. France (N.S.) 1989 119 133

[24] Hochster, M. Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes Ann. of Math. (2) 1972 318 337

[25] Hochster, M. Contracted ideals from integral extensions of regular rings Nagoya Math. J. 1973 25 43

[26] Hochster, Melvin Topics in the homological theory of modules over commutative rings 1975

[27] Hochster, Melvin Big Cohen-Macaulay modules and algebras and embeddability in rings of Witt vectors 1975 106 195

[28] Hochster, Melvin Cyclic purity versus purity in excellent Noetherian rings Trans. Amer. Math. Soc. 1977 463 488

[29] Hochster, Melvin Some applications of the Frobenius in characteristic 0 Bull. Amer. Math. Soc. 1978 886 912

[30] Hochster, Melvin Cohen-Macaulay rings and modules 1980 291 298

[31] Hochster, Melvin Canonical elements in local cohomology modules and the direct summand conjecture J. Algebra 1983 503 553

[32] Hochster, M., Eagon, John A. Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci Amer. J. Math. 1971 1020 1058

[33] Hochster, Melvin, Roberts, Joel L. Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay Advances in Math. 1974 115 175

[34] Hochster, Melvin, Roberts, Joel L. The purity of the Frobenius and local cohomology Advances in Math. 1976 117 172

[35] Huneke, Craig Hilbert functions and symbolic powers Michigan Math. J. 1987 293 318

[36] Huneke, Craig An algebraist commuting in Berkeley Math. Intelligencer 1989 40 52

[37] Itoh, Shiroh Integral closures of ideals generated by regular sequences J. Algebra 1988 390 401

[38] Itoh, Shiroh Integral closures of ideals of the principal class Hiroshima Math. J. 1987 373 375

[39] Kaplansky, Irving Commutative rings 1974

[40] Kempf, George The Hochster-Roberts theorem of invariant theory Michigan Math. J. 1979 19 32

[41] Kunz, Ernst Characterizations of regular local rings of characteristic 𝑝 Amer. J. Math. 1969 772 784

[42] Kunz, Ernst On Noetherian rings of characteristic 𝑝 Amer. J. Math. 1976 999 1013

[43] Lipman, Joseph Relative Lipschitz-saturation Amer. J. Math. 1975 791 813

[44] Lipman, Joseph, Sathaye, Avinash Jacobian ideals and a theorem of Briançon-Skoda Michigan Math. J. 1981 199 222

[45] Lipman, Joseph, Teissier, Bernard Pseudorational local rings and a theorem of Briançon-Skoda about integral closures of ideals Michigan Math. J. 1981 97 116

[46] Ma, Frank Splitting in integral extensions, Cohen-Macaulay modules and algebras J. Algebra 1988 176 195

[47] Mac Lane, Saunders Homology 1963

[48] Matsumura, Hideyuki Commutative algebra 1970

[49] Mehta, V. B., Srinivas, V. Normal 𝐹-pure surface singularities J. Algebra 1991 130 143

[50] Monsky, P. The Hilbert-Kunz function Math. Ann. 1983 43 49

[51] Nagata, Masayoshi Local rings 1962

[52] Northcott, D. G., Rees, D. Reductions of ideals in local rings Proc. Cambridge Philos. Soc. 1954 145 158

[53] Northcott, D. G., Rees, D. A note on reductions of ideals with an application to the generalized Hilbert function Proc. Cambridge Philos. Soc. 1954 353 359

[54] Peskine, C., Szpiro, L. Dimension projective finie et cohomologie locale. Applications à la démonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck Inst. Hautes Études Sci. Publ. Math. 1973 47 119

[55] Peskine, Christian, Szpiro, Lucien Syzygies et multiplicités C. R. Acad. Sci. Paris Sér. A 1974 1421 1424

[56] Ratliff, Louis J., Jr. Chain conjectures in ring theory 1978

[57] Rees, D. A note on asymptotically unmixed ideals Math. Proc. Cambridge Philos. Soc. 1985 33 35

[58] Rees, D. Reduction of modules Math. Proc. Cambridge Philos. Soc. 1987 431 449

[59] Roberts, Paul Two applications of dualizing complexes over local rings Ann. Sci. École Norm. Sup. (4) 1976 103 106

[60] Roberts, Paul Cohen-Macaulay complexes and an analytic proof of the new intersection conjecture J. Algebra 1980 220 225

[61] Roberts, Paul Homological invariants of modules over commutative rings 1980 110

[62] Roberts, Paul The vanishing of intersection multiplicities of perfect complexes Bull. Amer. Math. Soc. (N.S.) 1985 127 130

[63] Roberts, Paul Le théorème d’intersection C. R. Acad. Sci. Paris Sér. I Math. 1987 177 180

[64] Roberts, Paul Intersection theorems 1989 417 436

[65] Seibert, Gerhard Complexes with homology of finite length and Frobenius functors J. Algebra 1989 278 287

[66] Skoda, Henri Application des techniques 𝐿² à la théorie des idéaux d’une algèbre de fonctions holomorphes avec poids Ann. Sci. École Norm. Sup. (4) 1972 545 579

[67] Srinivas, V. Normal surface singularities of 𝐹-pure type J. Algebra 1991 348 359

[68] Szpiro, L. Sur la théorie des complexes parfaits 1982 83 90

[69] Wall, C. T. C. Lectures on 𝐶^{∞}-stability and classification 1971 178 206

[70] Watanabe, Keiichi Study of 𝐹-purity in dimension two 1988 791 800