Index
a-invariant, 181
acyclicity lemma, 220
acyclicity principle, 26
adjunction morphism, 46
Adolphson, Alan, 250, 251, 254
affine variety, 143
Stein, 196
algebraic set, 1
cone, 2
coordinate ring, 7
dimension, 7
hypersurface, 2
irreducible, 7
singular, 10
smooth, 10
tangent space, 10
Andre, Michel, 218
arithmetic rank, 101-103, 156, 201
Artin-Rees lemma, 59
associated prime, 69, 118
Auslander, Maurice, 94, 95
Auslander-Buchsbaum formula, 91
Avramov, Luchezar, 217
b- function
global, 243
local, 245
Baer's criterion, 257
Bass numbers, 118, 262
of Gorenstein rings, 123
Bass' conjecture, 119
Bass, Hyman, 117, 119, 260
Bass-Quillen conjecture, 30
Bernstein, Joseph, 175, 242, 243
Bernstein-Sato polynomial, 243, 245
Betti numbers, 90
big Cohen-Macaulay module, 223
Blickle, Manuel, 246
Brodmann, Markus, 147, 155
Buchberger's algorithm, 64, 177
Buchsbaum, David, 94, 95
canonical module, 126, 130
Bass numbers, 126
existence, 129, 184
global, 183, 184, 189
graded, 142
Stanley-Reisner ring, 167
uniqueness, 130, 185
Cartan, Henri, 15
Cattani, Eduardo, 251
Cayley-Hamilton theorem, 12
Cech cohomology, 20, 21, 27, 73, 84
Cech complex, 20, 73
refinement, 21
sign rule, 20
Cech-de Rham complex, 197
Chevalley's theorem, 148
Chevalley, Claude, 148
Cohen's structure theorem, 96
Cohen, Irvin, 96
Cohen-Macaulay ring, 93, 105, 119
local cohomology, 115
cohomological dimension, 100, 101, 103,
147, 200, 227
commutator, 171
complete intersection ring, 106, 121
complex
bounded, 32
comparison theorem, 35
dualizing, 183
Horn, 32
277
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