Index
affinoid
algebra, 409
Berkovich, 9
open, xx, 9, 29
strict closed, 9, 29, 127, 140
strict open, 9
subdomain, 410
algebraically capacitable, ix, xxiii, 142,
181
analytic component, 364
annular segment, 274
annulus, 27
Berkovich, 41, 265, 281
open, 283
rational, 283
standard open, 284
Arakelov-Green’s function, xxv, 225,
241, 246, 299, 305, 307, 375
arbre, 147
arc, 393
arcwise connected, see also
path-connected
attracting basin, 320, 337, 365
Attracting Fixed Point Theorem, 350
attracting periodic point, 319
Autissier, Pascal, xi, 191
Bx(v)−,
41
Baire set, 382
ball
closed, 76, 81, 84
open, 75, 81, 84
BDV(Γ), xxi, 57, 204
BDV(PBerk), 1 xxi
BDV(U), 97, 217
Benedetto, Rob, xi, 292, 293, 303, 335,
357, 362, 364, 366, 367, 370, 374
Berkovich
adelic neighborhood, 142, 178, 180
adelic set, 141, 178, 184, 186
affine line, xv, 19, 413
classification theorem, xvii, 3, 21
curves, x, xi, 49, 117
equicontinuity locus, xxvi, 333
hyperbolic space, xvii, 38
projective line, ix, xv, 24
spaces, x, xv, xxvi, 410, 413
Berkovich, Vladimir, xxvi, 18, 47, 147,
405
ezivin, J.-P., 354
Bilu’s equidistribution theorem, xxiv
boundary derivative, 235
boundary point, 56
bounded potentials, 109, 246–248
bout, 358
branch point, 394
branching, 12
countable, xiii
of main dendrite, 147, 197
uncountable, xiii
Call-Silverman local height, 295–297,
306
canonical distance, 83, 85
canonical height, 185, 306, 308
canonical measure, x, xii, xxvi, 240, 297
Cantor matrix, 156, 160
Cantor, David, 180
capacity, xxii
global, 141, 178, 179, 182, 186
logarithmic, xxii, 121
capped, 279, 281
Chambert-Loir, Antoine, x, 18, 191,
306, 374
Chebyshev constant, xxiii, 136
Christmas tree, inverted, 271
classical point, 5
cofinal, 379
coherent system of measures, 95, 98
completed residue field, 415
423
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