index 265

minimum metric, 6, 22, 23, 188

Minkowski, H., 3

model, 6, 25–28, 43, 46, 52, 57, 121, 122,

124, 127, 128, 146, 152, 153, 156, 158,

159, 187, 194, 208

modular operation, 177

Monte Carlo method, 50

Mordell’s conjecture, 38

Mordell’s examples of cubic surfaces, 4,

122, 132, 146

Mordell, L. J., 4, 8, 38, 122, 132

Moroz, B. Z., 79

Murre and Oort, theorem of, 108

Néron–Severi group, 108, 112

Néron–Severi torus, 63, 64

Noether–Lefschetz Theorem, 5, 186, 193

non-Archimedean valuation, 17

non-Azumaya locus, 90, 106, 128

non-obvious line, 10, 39, 196, 200

normalized valuation, 16

Northcott’s theorem, 18

numerical integration, 193

obvious line, 9, 39, 194, 196

open addressing, 171

Opteron processor, 182

order, 103–105

maximal, 103–106

p-adic measure, 51, 52

p-adic unsolvability, 36

p-adic valuation, 223

p-adic numbers, 2

page prime, 169, 170, 172, 177, 180

paging, 172

parametrization, 2

Pari, 192

partial presorting, 181

Pentium 4 processor, 183

periodicity isomorphism, for cohomology of

cyclic group, 154

Perron’s formula, 73

Peyre, E., 6, 8, 9, 33, 40, 47, 59–63, 66, 78,

165, 186, 187, 205, 208

Peyre’s constant, 6, 9, 10, 47, 59–61, 63,

165, 185, 187, 189, 200, 205, 206, 219,

231, 233

Peyre’s Tamagawa type number, see

Peyre’s constant

Picard functor, 108

Picard group, 112

Picard rank

of cubic surface, 117

Picard scheme, 108

Poincaré residue map, 55

polymake, 50

Poonen, B., 125

post-processing, 178

prefetch, 179

presorting, partial, 180

Preu, T., 132

principal divisor

norm of, 154

product formula, 16

projective plane, 198

Puiseux expansion, 193

pullback

of Azumaya algebra, 91

pure cubic field

discriminant of, 215, 237

quadratic form, 174–176, 178

quadratic reciprocity low, 4

quadric, 198

quartic surface

diagonal, 42

quartic threefold, 9, 10, 62, 185–207

diagonal, 9, 10, 37, 47

Quicksort, 180

Radix sort, 180

rational points

Brauer–Manin obstruction to, 125

rational surface, 110, 112, 113, 115, 196

rational variety, 166

reading, 175–177, 181, 182, 200

reciprocity low

biquadratic, 4

cubic, 4, 161

quadratic, 4

reduced trace, 103

restriction, 151

Riemann zeta function, 222

ruled surface, 194, 196, 199

ruled variety, 166

Salberger, P., 65

Sansuc, J.-J., 9, 61, 65, 122, 146–148, 206,

220, 234

Schappacher, N., 1, 239

Schmidt, W. M., 63

Schröer, S., 106

search bound, 9, 182, 200, 209

searching for rational points, see searching

for solutions of Diophantine equation

searching for solutions of Diophantine

equation, 9, 169–182, 200

naive, 169

selection of bits, 176

Selmer, E. S., 37, 122