On the Iwasawa algebra for pro-l Galois groups
نویسندگان
چکیده
منابع مشابه
Computing Pro-P Galois Groups
We describe methods for explicit computation of Galois groups of certain tamely ramified p-extensions. In the finite case this yields a short list of candidates for the Galois group. In the infinite case it produces a family or few families of likely candidates.
متن کاملIwasawa invariants of galois deformations
of the absolute Galois group of a number field F . Assume that ρ̄ is ordinary in the sense that the image of any decomposition group at a place v dividing p lies in some Borel subgroup Bv of G. Assume also that ρ̄ satisfies the conditions of [11, Section 7] which guarantee that it has a reasonable deformation theory; see Section 3.1 for details. In this paper we show that the Iwasawa invariants o...
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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
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...
متن کاملRandom 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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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2012
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-012-0984-1