index 263
Eckardt point, 194
Edidin, D., 107
effective cone, 47–49
Eisenstein polynomial, 134
elementary symmetric functions, 19, 212
elliptic cone, 194
elliptic curve, 154
elliptic surface, 166
Elsenhans, A.-S., 165, 185, 205
Emerson, R. W., 205
Enriques surface, 110
equidistribution, 5, 158, 188, 205
Essouabri, D., 80
étale cohomology, 45, 57, 83, 102
étale morphism, 51, 53
étale neighbourhood, 96, 108, 111
étale topology, 93, 96, 99, 101
Euler product, 190, 192, 220, 221
Euler sequence, 55
exponential sequence, 45, 109
factor α, 4, 6, 47–50, 56, 60, 61, 187, 188,
207, 210, 231
factor β, 6, 50, 187, 207, 210, 231
faithful flat descent, 93
Faltings, G., 15, 25, 38
Fano variety, 2, 4, 6, 9, 37, 38, 40, 41, 43,
44, 46, 47, 58, 59, 61, 165, 185, 186,
188, 205
Fano variety
almost, 66
Faraday, M., 119
Fermat cubic, 37
FFT convolution, 189
FFT point counting, 192, 200
Forster, O., 183
Fouvry, È, 79
fpqc-topology, 93
Fröhlich, A., vii
Franke, J., 3, 47, 77, 78
Frei, F., 80
Frobenius eigenvalues, 58, 212
Fubini-Study metric, 22, 24
fundamental finiteness, 6, 10, 15, 16, 25,
209, 222, 233
G-set, 114
Gabber, O., 106
Galois cohomology, 83
Galois descent, 64, 87
GAP, 7, 48, 49, 116, 144, 210, 239, 241
Gauß–Legendre formula, 193
Gauß sum, 213
Generalized Riemann Hypothesis, 233, 236,
237
genus one curve, 137, 146, 153, 155, 156,
166, 198, 199
Gilbert, W. S., 185
Gillet, H., 25, 33
global class field theory, 4, 107, 111
global evaluation map, see Manin map
gluing data, 93, 96, 127
Godeaux surface, 39
good
reduction, 168, 211, 213, 227
Gröbner base, 144, 145
Grothendieck, A., 6, 83, 98, 106
Guy, M. J. T., 4, 122
Hankel, H., 1
Harari, D., 132
hardware, 176
Hardy, G. H., 3
Hartshorne, R., vii
hash function, 170, 177, 180
hash table, 171, 180, 181, 200
hashing, 9, 170, 180, 222
uniform, 170
Hasse principle, 3–5, 8, 122, 125, 132, 205,
221
Brauer–Manin obstruction to, 8, 36, 61,
125, 132, 140–142, 148
counterexample to, 8, 122, 141, 142
Hasse’s bound, 137, 156
Hasse, H., 3, 205
Hassett, B., 107
Hawking, S., 15
Heath-Brown’s congruences, 161
Heath-Brown, D. R., 5, 61, 62, 66–68, 79,
161, 165, 233
Hecke L-function, 216
Hecke theta function, 217, 218
height
absolute, 18, 20, 30, 45
adelic, 29
anticanonical, 3, 40, 45, 59, 205
canonical, 3, 40, 45, 59, 205
defined by adelic metric, 45
defined by an invertible sheaf, 6, 20
l2,
24
logarithmic, 20, 23
naive, 3, 6, 15, 16, 18, 23, 186–188, 205,
233
of smallest point, 10
with respect to hermitian line bundle, 6,
23
Hensel’s lemma, 2, 52, 94–96, 102, 124, 133,
137, 153, 157, 173, 235
Hensel, K., 2
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