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(P1 Berk ), 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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