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