A Brief Introduction to Classical and Adelic Algebraic ... - William Stein

Index
1-ideles, 169
I divides product of primes lemma, 33
I ∩ J = IJ lemma, 57
K + and K∗ are totally disconnected
lemma, 135
N-adic distance, 121
N-adic numbers, 122
N-adic valuation, 121
N-distance is metric proposition, 121
R-module, 19
A +
K
and base extension corollary, 159
A +
K /K+ has finite measure corollary,
162
Norm(aI) lemma, 66
OK is Dedekind proposition, 32
OK is Noetherian corollary, 29
OK is a lattice proposition, 28
OK is integrally closed proposition, 31
OK span and OK ∩ Q = Z lemma, 27
QN totally disconnected proposition,
124
Z is a PID proposition, 22
Z is a ring proposition, 26
e, f, g proposition, 98
p-adic field, 123
Magma, 9, 10, 26, 31, 35, 37–41, 43,
46, 50, 53, 55, 58, 65, 71, 82,
84, 85, 88, 92, 95, 130, 174,
176, 177
abelian groups
structure theorem, 15
adele ring, 158
adic-expansion lemma, 130
algebraic integer, 25
Algebraic number theory, 10
185
almost all, 155
any two norms equivalent lemma, 138
archimedean, 110
Artin symbol, 102
ascending chain condition, 20
base extension of adeles lemma, 159
Birch and Swinnerton-Dyer conjecture,
125
Blichfeld lemma, 68
Blichfeldt’s lemma, 80
Cauchy sequence, 119
characterization of discrete lemma, 111
characterization of integrality proposition,
26
characterization of Noetherian proposition,
20
chinese remainder theorem, 58
class group, 67, 171
class group generated by bounded primes
lemma, 73
cokernel, 16
compact quotient of adeles theorem,
160
compact quotient of ideles theorem,
170
compact subset of adeles corollary, 161
compactness of ring of integers theorem,
131
complete, 119, 119
complete embedding theorem, 119
complete local field locally compact corollary,
131
completion, 119
completion, norms, and traces corollary,
143