Extensions of number fields with wild ramification of bounded depth
| dc.creator | Hajir, Farshid | |
| dc.creator | Maire, Christian | |
| dc.date | 2001-12-04 | |
| dc.date.accessioned | 2026-07-07T04:45:36Z | |
| dc.date.available | 2026-07-07T04:45:36Z | |
| dc.description | We consider p-extensions of number fields such that the filtration of the Galois group by higher ramification groups is of prescribed finite length. We extend well-known properties of tame extensions to this more general setting; for instance, we show that these towers, when infinite, are ``asymptotically good'' (an explicit bound for the root discriminant is given). We study the difficult problem of bounding the relation-rank of the Galois groups in question. Results of Gordeev and Wingberg imply that the relation-rank can tend to infinity when the set of ramified primes is fixed but the length of the ramification filtration becomes large. We show that all p-adic representations of these Galois groups are potentially semistable; thus, a conjecture of Fontaine and Mazur on the structure of tamely ramified Galois p-extensions extends to our case. Further evidence in support of this conjecture is presented. | |
| dc.identifier | https://arxiv.org/abs/math/0112319 | |
| dc.identifier | http://arxiv.org/abs/math/0112319 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63015 | |
| dc.subject | Number Theory | |
| dc.title | Extensions of number fields with wild ramification of bounded depth | |
| dc.type | text |