Index +(M), 13 M · N, 106 M | N, 3 Mart, 20, 42 Rh, 165 Rart, 20, 42 R, 41 R, 7 ⊥, 211 5 , 138 a-invariant, 98 abelian category, 1 Abhyankar, Shreeram, 101, 106 absolutely flat homomorphism, 167, 168 abstract hypersurface, 141, 150, 150–151, 298, 298, 299 action by linear changes of variable, 61, 62, 65, 69–72, 81, 83, 86, 118, 151, 152, 262 acyclic complex, 208, 216 addR(M), 13, 15, 26, 106, 163, 165, 230 additive category, 1, 2, 9, 10, 32 in which idempotents split, 1, 3–5 additive function, 91, 97 ADE Coxeter-Dynkin diagram, 81, 91–97, 101, 102, 104, see also extended ADE Coxeter-Dynkin diagram ADE hypersurface singularity, 42, 50–52, 81, 83, 87, 97, 133, 141, 146–161, 172–173, 229–232, 234–237, 295 (A1), 102, 103, 229, 291, 294, 295 (A2), 113 (A∞), 78, 241, 244, 245, 252–256, 259, 260, 262–264, 297, 301 (An), 77, 87, 90, 93, 119, 133, 146, 153, 236 (D4), 88, 103, 149, 294 (D∞), 78, 241, 244, 245, 252, 253, 256–260, 262, 263, 265, 297, 300, 301, 304 (Dn), 87, 90, 93, 149, 154, 236, 262 (E6), 88, 94, 148, 155, 234, 237 (E7), 88, 95, 149, 237 (E8), 89, 96, 148, 157, 237 adjoint pair, 71 adjunction formula, 101 aﬃne diagram, see extended ADE Coxeter-Dynkin diagram Akizuki, Yasuo, 316 algebra retraction, 77 algebraic closure, 117, 118, 173 algebraic duality, 203 algebraic field extension, 167, 174 algebraic fundamental group, see ´ etale fundamental group algebraic number field, 50 algebraically closed field, 51, 73, 90, 92, 98, 101, 118, 128, 133, 134, 137, 138, 141, 142, 144–147, 151, 159, 160, 163, 172, 192, 225, 234, 253, 259, 262, 268, 276, 277, 279–283, 285, 287, 288, 293, 299, 321, 323 almost split sequence, see Auslander-Reiten sequence analytic branch, 19, 146–149 analytic local ring, 241 analytically normal, 23, 24 355

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