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
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