On Galois groups of unramified pro-p extensions
نویسندگان
چکیده
منابع مشابه
CONSTRUCTION OF MAXIMAL UNRAMIFIED p-EXTENSIONS WITH PRESCRIBED GALOIS GROUPS
For any number field F (not necessary of finite degree) and prime number p, let Lp(F ) denote the maximal unramified p-extension over F , and put G̃F (p) = Gal(Lp(F )/F ). Though the structure of G̃F (p) has been one of the most fascinating theme of number theory, our knowledge on it is not enough even at present: It had been a cerebrated open problem for a long time whether G̃F (p) can be infinit...
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Galois groups of infinite p-extensions of number fields unramified at p are a complete mystery. We find by computer a family of pro-p groups that satisfy everything that such a Galois group must, and give evidence for the conjecture that these are the only such groups. This suggests that these mysterious Galois groups indeed have a specific form of presentation. There are surprising connections...
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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.
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We consider a ramified Galois cover φ : X̂ → Px of the Riemann sphere Px, with monodromy group G. The monodromy group over Px of the maximal unramified abelian exponent n cover of X̂ is an extension nG̃ of G by the group (Z/nZ), where g is the genus of X̂. Denote the set of linear equivalence classes of divisors of degree k on X̂ by Pic(X̂) = Pic. This is equipped with a natural G action. We show tha...
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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 ...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2008
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-008-0236-1