Index
2-extension, 13, 33
abelian field, 2
absolute Galois group, 5, 9, 10
adele, 4, 14
adele ring, 4
algebraic K-group, 5
Archimedean prime, 4
Artin conductor, 20, 21
Artin root number, 1, 2, 8, 16, 18, 21
augmentation ideal, 38, 98
class-group, 6
cohomologically trivial, 8, 11, 12, 14
commutator subgroup, 5
completion, 22
conductor, 2
decomposition group, 14, 16, 20
direct sum, 5
discriminant, 20
extended Artin L-function, 8
extension of scalars, 5
fundamental 2-extension, 34
fundamental class, 32, 33
Gauss sums, 21
Gaussian integers, 11
Grothendieck group, 6
Horn-description, 72
idele, 4, 5
integral quaternions, 10, 99
irreducible, 2
Jacobi symbol, 21
kernel group, 7
local Chinburg invariant, 14
local class field theory, 3, 98
local root number, 21, 124
locally free, 5
norm, 98
number field, 4
order, 7
orthogonal, 9
orthogonal representation, 21
prime element, 29
primitive root of unity, 5, 10
projective, 5
quaternion group, 9, 28
quaternions, 7
rational quaternions, 38
representation, 20
representation ring, 4
resolvent, 17, 70
restricted product, 4
root number class, 1, 16
second Chinburg invariant, 1, 15
splitting field, 70
Swan module, 8, 10
symplectic, 2, 7
symplectic representation, 1
tame, 14, 15
totally positive, 7, 20
units, 34
weak product, 6, 17
wild, 14
wildly ramified, 1
maximal order, 2, 7
maximal unramined extension, 32
133
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