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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