Random pro-$p$ groups, braid groups, and random tame Galois groups
نویسندگان
چکیده
منابع مشابه
Random pro-p groups, braid groups, and random tame Galois groups
In this article we introduce a heuristic prediction for the distribution of the isomorphism class of GS(p), the Galois group of the maximal pro-p extension of Q unramified outside of S, where S is a ”random” set of primes. That these groups should exhibit any statistical regularity is not at all obvious; our expectations in this direction are guided by the Cohen-Lenstra conjectures, which (amon...
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Fix a prime p, a number field K, and a finite set S of places of K none of which has residue characteristic p. Fix an algebraic closure K of K and let KS be the maximal p-extension of K inside K which is unramified outside S; it is the compositum of all finite p-power degree extensions of K unramified outside S. We assume that real places of K not contained in S do not complexify in the extensi...
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Let p be a prime. It is a fundamental problem to classify the absolute Galois groups GF of fields F containing a primitive pth root of unity ξp. In this paper we present several constraints on such GF , using restrictions on the cohomology of index p normal subgroups from [LMS]. In section 1 we classify all maximal p-elementary abelian-by-order p quotients of these GF . In the case p > 2, each ...
متن کاملTAME PRO-p GALOIS GROUPS: A SURVEY OF RECENT WORK par
Fix a prime p, a number field K, and a finite set S of places of K none of which has residue characteristic p. Fix an algebraic closure K of K and let KS be the maximal p-extension of K inside K which is unramified outside S; it is the compositum of all finite p-power degree extensions of K unramified outside S. We assume that real places of K not contained in S do not complexify in the extensi...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2011
ISSN: 1661-7207
DOI: 10.4171/ggd/127