266 index
Serre, J.-P.
theorem of, 86
sheaf of Azumaya algebras, 6, 89
Siegel’s estimate, 223
Siegel, C. L., 63, 205, 223
similarity
of Azumaya algebras, 93, 94, 98
of central simple algebras, 84
singular cohomology, 83
64-bit processor, 176
Skolem–Noether theorem, 85, 95, 96
Slater, J. B., 68
Smart, N. P., 166
solutions of Diophantine equation
algorithm to search for, 9, 169–182, 200
naive, 169
sorting, 180, 222
Soulé, C., 25, 33
splitting field, 85, 102
sporadic line, 10, 39, 196, 200
Stark, H. M., 223
statistical parameters, 201, 202
Steiner surface, 199
Strauch, M., 78
Sullivan, A., 185
surface, 47, 106, 115, 193
abelian, 196
algebraic, 98, 106
bielliptic, 166, 196
cubic, 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
Del Pezzo, 50, 65, 66, 161
weak, 66, 67, 79
elliptic, 166
Enriques, 110
Godeaux, 39
in P3, 9
K3, 9, 41–43, 110, 115, 167, 168, 196
Kummer, 41
non-minimal, 43
non-separated, 107
of general type, 39, 195, 196
of Kodaira dimension one, 196
of Kodaira dimension zero, 41
rational, 110, 112, 113, 115, 196
ruled, 194, 196, 199
Steiner, 199
surfaces
classification of, 167
suspicious
pair, 197, 198
point, 195, 196
Swinnerton-Dyer’s list, 151
Swinnerton-Dyer, Sir Peter, 4, 7–9, 68, 79,
117, 122, 142, 151, 167, 172, 202
Tamagawa measure, 56, 188, 208
Tamagawa number, see Peyre’s constant
Tate, J., 159
Tate cohomology, 115
Tate’s algorithm, 159
tensor field, 53
test for conic through two points, 197
theorem
Hilbert 90, 88, 99, 111, 131
of Auslander and Goldman, 7, 98, 103,
105
of Bezout, 194
of Colliot-Thélène, Kanevsky, and
Sansuc, 147, 148
of Legendre, 3, 205
of Lichtenbaum, 113
of Linnik, 233
of Murre and Oort, 108
of Noether and Lefschetz, 186, 193
of Northcott, 18
of Serre, 86
of Skolem and Noether, 85, 95, 96
of Tietze, 25, 32
of Tsen, 110
of Zak, 195
weak Lefschetz, 189
Thompson, S., 35
threefold, 36, 206
cubic, 9, 10, 39, 62, 185–203
diagonal, 9, 10, 36, 37, 47
quartic, 10, 62, 185–207
diagonal, 9, 10, 37, 47
Tietze’s theorem, 25, 32
toric variety, 78, 79
torsor, universal, 63–71
transcendental Brauer–Manin obstruction,
5, 132
Tschinkel, Y., 3, 6, 8, 47, 61, 62, 66, 67,
77–79, 165
Tsen’s theorem, 110
27 lines on cubic surface, 7, 48–51,
115–117, 125, 144–146, 149, 160,
209–213, 234, 239
Tychonov topology, 121
universal torsor, 63–71
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