Index
absolute value, 168
archimedian, 172
associated to a valuation, 170
extension of, 171, 172
equivalent, 175
non-archimedian, 172
trivial, complex, 168
absolutely irreducible polynomial,
236
admissible product, 278, 279
admissible sum, 278
affine,
curve, 65
line, 35, 66
plane, space, 35
affine chart, 200
algebraic integer, 7, 10
algebraically closed in L, 236
Arakelov theory, 323
Artin-Schreier extension, 86, 109
automorphism of a curve, 245
base change, 243
Belyi's Theorem, 252
Bezout's Theorem, 43, 222
blowup of a point, 76
branch locus, 102, 248
branched cover, 103
canonical divisor class, 289, 319, 327,
337
chain of primes, 28
change of coordinates, 203, 209
character, 293, 295
characteristic, 11, 26, 56
Chinese Remainder Theorem, 92, 116
circuit, 36
class field theory, 109
class group,
in additive form, 260
compact ified, 321
divisor class group, 261
ideal class group, 159, 296, 341
class number
of a curve, 285
of a number field, 164, 275
Clifford's Theorem, 317
cofinal subset, 381
387
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