Index
abelian surface, 196
abelian variety, 41, 166
Abramovich, D., 39
accumulating subvariety, 9, 36, 195, 196,
199
accumulating surface, 196, 199
adelic intersection product, 33
adelic metric, 27, 31, 45, 46
adelic Picard group, 25, 27, 30, 33
adelic point, 4–8, 10, 56, 61, 119–121, 124,
137, 145, 206, 208, 231
adelic topology, 121
adelically metrized invertible sheaf, 27–31,
33
adjunction formula, 55
affine cone, 54
algebraic Brauer–Manin obstruction, 5, 132
algebraic surfaces, 98, 106
classification of, 167
algorithm
FFT point counting, 190, 192, 200
for computation of volume, 50
for numerical integration, 193
obvious, 189
of Tate, 159
to compute approximate value for
Peyre’s constant, 192
to detect conics on quartic threefold, 198
to detect lines on cubic threefold, 196,
200
to search for solutions of Diophantine
equation, 9, 169–182, 200
naive, 169
to solve system of equations over finite
field, 196, 198
to test for conic through two points, 197
to test lines for irrationality, 195
to test lines for irrationality, 196
to test whether conic is contained in
quartic threefold, 198
almost Fano variety, 66
AMD, 182
Amir-Moez, A. R., 83
Arakelov, S. Yu., 25
Arakelov degree, 6, 22
Archimedean valuation, 17
ARIBAS, 183
arithmetic cohomology, 83
arithmetic degree, 30
arithmetic intersection theory, 21
arithmetic Picard group, 21
arithmetic variety, 6, 21, 23–25
Artin conductor, 215, 236
Artin L-function, vii, 51, 207, 208, 216,
222, 231
assembly, 179
Auslander–Goldman, theorem of, 7, 98,
103, 105
automorphisms of
PN
, 20
Azumaya algebra, 83, 89–98, 104–106, 123,
124, 128
bad
prime, 192
reduction, 153
Batyrev, V. V., 33, 40, 66, 78, 79
Batyrev and Manin, conjecture of, 6, 38,
40–43, 166, 196
Bernstein, D., 166, 199
Bezout’s theorem, 194
Bhowmik, G., 80
bielliptic surface, 166, 196
Bierce, A., 165
Billard, H., 41
biquadratic reciprocity low, 4
Bogomolov, F., 42
conjecture of, 42
Bombieri, E., 47
Bourbaki, N., 29
Brauer, R., 84
261
Previous Page Next Page