Geodesic
On tame ${\mathbb {Z}}/p{\mathbb {Z}}$-extensions with prescribed ramification
Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 40-48

Voir la notice de l'article provenant de la source Cambridge

DOI

The tame Gras–Munnier Theorem gives a criterion for the existence of a $ {\mathbb Z}/p{\mathbb Z} $-extension of a number field K ramified at exactly a tame set S of places of K, the finite $v \in S$ necessarily having norm $1$ mod p. The criterion is the existence of a nontrivial dependence relation on the Frobenius elements of these places in a certain governing extension. We give a short new proof which extends the theorem by showing the subset of elements of $H^1(G_S,{\mathbb {Z}}/p{\mathbb {Z}})$ giving rise to such extensions of K has the same cardinality as the set of these dependence relations. We then reprove the key Proposition 2.2 using the more sophisticated Greenberg–Wiles formula based on global duality.
DOI : 10.4153/S0008439523000498
Mots-clés : Tame ramification, Z/pZ-extension, Gras–Munnier Theorem, Frobenius automorphism 
Hajir, Farshid; Maire, Christian; Ramakrishna, Ravi. On tame ${\mathbb {Z}}/p{\mathbb {Z}}$-extensions with prescribed ramification. Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 40-48. doi: 10.4153/S0008439523000498
@article{10_4153_S0008439523000498,
     author = {Hajir, Farshid and Maire, Christian and Ramakrishna, Ravi},
     title = {On tame ${\mathbb {Z}}/p{\mathbb {Z}}$-extensions with prescribed ramification},
     journal = {Canadian mathematical bulletin},
     pages = {40--48},
     year = {2024},
     volume = {67},
     number = {1},
     doi = {10.4153/S0008439523000498},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000498/}
}
TY  - JOUR
AU  - Hajir, Farshid
AU  - Maire, Christian
AU  - Ramakrishna, Ravi
TI  - On tame ${\mathbb {Z}}/p{\mathbb {Z}}$-extensions with prescribed ramification
JO  - Canadian mathematical bulletin
PY  - 2024
SP  - 40
EP  - 48
VL  - 67
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000498/
DO  - 10.4153/S0008439523000498
ID  - 10_4153_S0008439523000498
ER  - 
%0 Journal Article
%A Hajir, Farshid
%A Maire, Christian
%A Ramakrishna, Ravi
%T On tame ${\mathbb {Z}}/p{\mathbb {Z}}$-extensions with prescribed ramification
%J Canadian mathematical bulletin
%D 2024
%P 40-48
%V 67
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000498/
%R 10.4153/S0008439523000498
%F 10_4153_S0008439523000498

Cité par Sources :