On pro-$p$ link groups of number fields
نویسندگان
چکیده
منابع مشابه
COHOMOLOGY OF NUMBER FIELDS AND ANALYTIC PRO-p-GROUPS
In this work, we are interested in the tame version of the Fontaine–Mazur conjecture. By viewing the pro-p-proup GS as a quotient of a Galois extension ramified at p and S, we obtain a connection between the conjecture studied here and a question of Galois structure. Moreover, following a recent work of A. Schmidt, we give some evidence of links between this conjecture, the étale cohomology and...
متن کاملSOME NOTES ON COHOMOLOGY OF NUMBER FIELDS AND ANALYTIC PRO-p-GROUPS by
In this paper, we are interested in the tame version of the Fontaine-Mazur conjecture. After recalling the role of étale cohomology in the context of this conjecture, we establish a relationship between it and the computation of the cohomological dimension of the pro-p-groups GS that appear. We then look at this conjecture by viewing the pro-pproup GS as a quotient of a Galois group with rami c...
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The modern theory of class field towers has its origins in the study of the p-class field tower over a quadratic imaginary number field, so it is fitting that this problem be the first in the discipline to be nearing a solution. We survey the state of the subject and present a new cohomological condition for a quadratic imaginary number field to have an infinite p-class field tower (for p odd)....
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In the 1970s, Isaacs conjectured that there should be a logarithmic bound for the length of solvability of a p-group G with respect to the number of different irreducible character degrees of G. So far, there are just a few partial results for this conjecture. In this note, we say that a pro-p group G has property (I) if there is a real number D = D(G) that just depends on G such that for any o...
متن کاملA note on free pro-p-extensions of algebraic number fields
For an algebraic number field k and a prime p, define the number p to be the maximal number d such that there exists a Galois extension of k whose Galois group is a free pro-p-group of rank d. The Leopoldt conjecture implies 1~ p ~ r2 +1, (r2 denotes the number of complex places of k). Some examples of k and p with 03C1 = r2 + 1 have been known so far. In this note, the invariant 03C1 is studie...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2019
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7787