Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of number fields with wild ramification of bounded depth   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.

29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs