262 index
Brauer group, 4–7, 83, 84, 94, 98, 99,
101–103, 105–117
cohomological, 7, 98–103, 105–117
of cubic surface, 116
Brauer–Manin obstruction, 5, 7–9, 36, 59,
61, 117, 123–125, 129, 132, 140, 146,
160, 161, 187, 188, 206–208
algebraic, 5, 132
is the only obstruction, 125
to rational points, 125
to the Hasse principle, 8, 36, 61, 125,
132, 140–142, 148
to weak approximation, 10, 125, 140,
141, 145, 148
transcendental, 5, 132
Brauer–Severi variety, 122
Bremner, A., 4, 122
Bright, M. J., 161, 166
Browning, T. D., 66, 67
Brüdern, J., 175
bucket sort, 180
buffer, 181, 182
C, 179, 183
Cantor, M., 239
Cassels, J. W. S., vii, 4, 122
Cayley’s cubic surface, 66
Čech cocycle, 96
Čech cohomology, 96, 97
center, 84, 89, 90
central simple algebra, 84, 85, 89–91, 101,
103
index of, 84
that splits, 85, 86
Chambert-Loir, A., 78
Chebotarev density theorem, 214, 236
Chebyshev’s inequalities, 235
Chinese remainder theorem, 177, 180, 181
circle method, 3, 5, 60–62, 187
class number formula, 223
classification of algebraic surfaces, 167
clustering, 171
cocycle, 86, 87
cohomologous to another, 86
cocycle relations, 127
local in étale topology, 93
cohomological Brauer group, 7, 98–103,
105–117
Colliot-Thélène, J.-L. , 5, 9, 61, 65, 122,
125, 146–148, 206, 220, 221, 234
conjecture of, 125
Colliot-Thélène, Kanevsky, and Sansuc,
Theorem of, 147, 148
collision, 171
conductor-discriminant formula, 215
congruence, 2, 9, 60, 161, 167–178, 180,
181, 183, 235
conic, 197–199
conjecture
of Batyrev and Manin, 6, 38, 40–43, 166,
196
of Bogomolov, 42
of Colliot-Thélène, 125
of Lang, 2, 6, 37–39, 166, 196
geometric, 38
strong, 38
weak, 38, 40
of Manin, 3, 6, 38, 46, 47, 63, 65, 67, 165,
185–188, 197, 201, 202, 205
of Manin and Peyre, 59, 61, 66, 67, 202
of Mordell, 38
control function, 177, 180
convolution, 189, 190
Corn, P. K., 7, 117
Cox ring, 64
Cox, D. A., 64
cubic threefold, 9
cubic reciprocity low, 4, 161
cubic surface, 4–8, 10, 47–51, 56, 61, 62,
115–117, 122, 125, 132, 140, 143–148,
159, 160, 165, 193, 194, 197, 237, 239
Cayley’s, 66
diagonal, 10, 122, 146–148, 159, 205–216,
237
general, 125
minimal, 234
cubic threefold, 9, 10, 39, 62, 185–203
diagonal, 9, 10, 36, 37, 47
cusp, 194
de Jong, A. J., 106
de la Bretèche, R., 66, 79
decoupled equation, 9, 171, 199
Dedekind zeta function, 191, 223
Del Pezzo surface, 50, 65, 66, 161
weak, 66, 67, 79
Deligne, P., 58, 168, 189
Derenthal, U., 50, 64, 66, 67, 80
descent
faithful flat, 93
Galois, 64, 87
descent method, 63–77
Diophantine equation, 1, 2, 4, 6, 9, 15, 165,
169–182, 199, 200
decoupled, 9, 171, 199
Diophantus, 1, 239
Dirichlet character, 222
distance, 28, 29
Duke, W., 236
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