INDEX 357 Cartan, Henri, 62 case analysis, dreary, 33 Cauchy sequence, 6, 244 Cauchy’s Theorem, 86 Caviglia, Giulio, 120 Cayley-Hamilton Theorem, 318 character, 73, 92–97, 153 character table, 94–96 characteristic bad, 64, 141, 159–160 five, 159 good, 51, 52, 83, 89–91, 133, 141, 144, 145, 151, 163, 172, 173, 234 three, 38, 49, 50, 59, 159 two, 36, 37, 41, 50, 128, 132–134, 137, 138, 140, 141, 145, 159, 160, 172, 253, 256, 259, 268, 280, 285, 288, 292, 297, 298 zero, 50, 98, 99, 109, 116–119, 151, 192, 293 characteristic polynomial, 30, 318, 335 Chern class c1, 105 Chevalley-Shephard-Todd Theorem, 69, 335, 339 Chinese Remainder Theorem, 318 Christensen, Lars Winther, 203, 210 C ¸imen, Nuri, 41, 45, 49, 50 Cl(R), 23 closed under AR sequences, 287–293 closed under extensions, 211, 212, 214, 215 clutter, 27, 47 codepth, 177, 178, 184, 185, 187–189, 193, 196, 208 coefficient field, 299 Cohen’s Structure Theorems, 177, 275 Cohen-Macaulay type, 116, 193 coherent sheaf, 98, 104, 106 cohomology, 64, 98, 105 complete intersection, 116 complete local ring is Henselian, 6 satisfies Krull-Remak-Schmidt, 7 complete resolution, 207–209 complex numbers C, 24, 81, 83–87, 89, 90, 93–97, 107, 119, 151–158, 241, 284 conductor c, 42, 47, 48, 59, 60, 245–252, 254–257, 264, 283 conductor square, 20, 42, 47, 48, 51, 53, 58, 59, 245, 283 conormal module I/I2, 116 constant rank, 19, 23, 43–45, 49–51, 57, 184, 188–189, 268, 284, 299–306, 316, 317 of a module over an Artinian pair, 32 countable CM type, 132, 133, 141, 241–266, 268, 284, 302 countable prime avoidance, 241–243 countably simple singularity, 141, 142–144, 245, 253, 259, 260, 297 covariants, 72, 152 cover, 211, 212 D, 86 DA(B), 328 Dade’s construction, 21, 28, 37 Dade, Everett C., 37 de la Pe˜ na, Jos´ e Antonio, 268, 270 decomposition group, 338–339 Dedekind different, 328–330, 336 Dedekind domain, 2, 10, 14 defects of an exact sequence, 239 deformation theory, 160 Del Pezzo-Bertini Theorem, 295 delta-invariant, 192 δ-invariant, 175, 190, 189–200 depth, 309, 309–310 Depth Lemma, 65, 66, 166, 178, 188, 246, 250, 310, 312, 329 derivation, 323 derivative, 20, 59 partial, 89, 192, 275 descent from the completion, 17 of bounded CM type, 297, 298, 303, 306, 307 of direct summands, 9 of finite CM type, 48, 133, 138, 163, 171, 279, 280 of finite representation type, 38 of isomorphism, 9
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