Index
a-number, 143
abelian scheme, 14, 46, 47
dual, 36
isogeny, 37
polarization, 37
abelian variety
absolutely simple, 15
and primary extension of fields, 15
isotypic, 22, 23, 31
lifting to characteristic 0, 86
Poincar´ e reducibility, 16
simple over a field, 15
abelian variety with sufficiently many
complex multiplication, 24, 25, 77
Grothendieck’s theorem in char. p 0,
79
refinement, 86
admissible algebraic homomorphism, 301
and Weil numbers, 315
construction of, 316
field of moduli, 310
primitive, 299
weight of, 303
Albert algebra, 28
classification of, 29
algebraic Hecke character, 118
algebraic part of, 119
and complex multiplication, 127, 128
compatible system of -adic characters
attached to, 121
construction by surgery procedure, 124
equivalent definition, 120
existence over field of moduli, 311
existence theorem, 305
formula for, see Shimura Taniyama
formula, for an algebraic Hecke
character
weight of, 300
α-group scheme, 142
Dieudonn´ e module of, 358–359
bad
p-adic place, 208, 208, 209, 210, 246
pair, 209, 235, 236, 238
Barsotti-Tate group, see also p-divisible
group
truncated, see also truncated
Barsotti-Tate group
truncated at level 1, 144
Brauer group, 18
of a global field, 20
order of an element of, 20
of a local field, 19
Cartier dual, 34, 326
Cartier theory, 351–353
Cartier module, 322, 352
V -flat, 352
V -reduced, 352
Cartier ring, 351
and the smooth formal group W , 351
central simple algebra, 16
Wedderburn’s theorem, 17
CM abelian variety, 23, 32
descent to a number field, 67
existence over field of moduli, 311
isotypic, 31
L-function of, 272
potential good reduction, 78
CM algebra, 26
CM field, 26
CM formal abelian scheme
criterion for algebraicity, 106
CM lifting
of a p-divisible group, 169
CM lifting questions, 86
after finite residue field extension (R), 88
CM lifting (CML), 87
sufficient condition, 102
Lie type of the closed fibers of CM
abelian schemes isogenous to a CM lift
(LTI), 210
strong CM lifting (sCML), 88, 210
to normal domains up to isogeny (IN), 88
local method, 178
necessary and sufficient condition, 100,
128–136
385
Previous Page Next Page