The Neukirch–Uchida theorem with restricted ramification
Let be a number field and a set of primes of . We write for the maximal extension of unramified outside and for its Galois group. In this paper, we prove the following generalization of the Neukirch–Uchida theorem under some assumptions: “For , let be a number field and a set of primes of . If and a...
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| Published in | Journal für die reine und angewandte Mathematik Vol. 2022; no. 785; pp. 187 - 217 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
De Gruyter
01.04.2022
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| Online Access | Get full text |
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| Summary: | Let
be a number field and
a set of primes of
.
We write
for the maximal extension of
unramified outside
and
for its Galois group.
In this paper, we prove the following generalization of the Neukirch–Uchida theorem under some assumptions:
“For
, let
be a number field and
a set of primes of
. If
and
are isomorphic, then
and
are isomorphic.”
Here the main assumption is that the Dirichlet density of
is not zero for at least one
. A key step of the proof is to recover group-theoretically the
-adic cyclotomic character of an open subgroup of
for some prime number |
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| ISSN: | 0075-4102 1435-5345 |
| DOI: | 10.1515/crelle-2021-0090 |