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