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Decomposition group of a prime and local Galois group
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Absolute value on a field
Extension of an absolute value
Local factorization and extended absolute values
Completion of a number field at a prime ideal
Transitivity of the Galois action on primes
Decomposition group
2026-09-28
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Restriction to completions gives
a
canonical
isomorphism
G
P
/
p
≅
Gal
(
L
P
/
K
p
)
.
(1)
Consequently the
number
of primes above
p
is the index of the
decomposition group
.
Ancestors
(11)
Decomposition group
Transitivity of the Galois action on primes
Completion of a number field at a prime ideal
Local factorization and extended absolute values
Extension of an absolute value
Absolute value on a field
Non-Archimedean analysis
Arithmetic
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 136
/
4
/
b
/
Solution
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