Index
ψv-regular sequence, see also regular
sequence
wv, see also distinguished place wv
Abel map, 179, 181, 187, 391, 392, 409,
411, 417
adele ring, 193
affinoid
admissible, 398
affinoid domain, x, xviii
Berkovich affinoid, 7, 123, 128
domain, 398, 401
strict closed affinoid, 128–130
Akhiezer, Naum, 14
algebraic integer, xii, xiv, 27, 28, 30, 31, 33
totally real, ix, xii
algebraically capacitable, xviii, xix, 1, 2, 4,
5, 6, 20, 28, 39, 80, 91, 106, 114, 117,
119, 120, 125, 129, 131, 159
with respect to ζ, 80
algorithm to compute nonarchimedean
capacities, 22
analytically accessible, 89, 104–107, 116
apportionment in House of Representatives,
160
Arakelov functions, 74
Arakelov theory, xiii
arc, 334, 385
analytic, 378
circular, 58
smooth, 104, 105, 135
Argument Principle, 11, 261
Autissier, Pascal, xiii
Baker, Matthew, 5, 336
Balinski, Michael, 160
band
BandN (k), 214, 215, 219, 221, 233, 234,
237, 238, 239, 249, 250, 257, 259, 264,
269–272, 274, 280–284, 295, 296, 298,
301, 312, 313, 315–317
coefficients patched by bands, 191, 214,
216, 221, 231, 234, 237
simultaneously when char(K) = p 0,
231, 233–235
high-order, 295
barrier, 334
Basic Patching Lemma, 287, 291, 292, 309
basic well-distributed sequence, 98, 171
basis
L-rational, xv, 61, 64, 65, 66–69, 191,
197, 209, 211–213, 219, 224, 230–232,
234, 243, 244, 247–249, 251, 257, 262,
263, 269, 271, 275, 280, 282, 299–301,
326–329
Lsep-rational,
64, 65, 66, 67–69, 197,
198, 224, 230, 231, 234, 235, 237, 238,
241, 243, 247, 248, 269, 280, 328
scaled L-rational, 242, 243, 246
Berkovich
adelic neighborhood, 6, 129
adelic set, 6, 7, 128, 129
analytic space, 5, 120, 336
analytification, 120, 125
closure, 121, 125, 128
compact set, 130
curve, xii, xix, 120, 122
Green’s function, 120, 125
neighborhood, 7, 128
open set, 7, 130
quasi-neighborhood, 6, 7, 128–130
strict closed affinoid, 7, 128, 130
topology, 6
Berkovich, Vladimir, 5, 120
Bertrandias, Fran¸ coise, xii
binomial theorem, 251
block, Galois
Block(i, j), 214, 220, 237, 238
coefficients patched block by block, 214,
219, 220
boundary, 111
equilibrium distribution supported on, 37
exceptional set contained in, 81
of filled Julia set, 19
piecewise smooth, xiii, 103, 105, 133,
135, 202, 249, 257, 261
Brouwer Fixed Point theorem, xv, xxi, 154
427
Previous Page Next Page