Arithmetic Lifting of Dihedral Extensions
نویسندگان
چکیده
منابع مشابه
Class Groups of Dihedral Extensions
Let L/F be a dihedral extension of degree 2p, where p is an odd prime. Let K/F and k/F be subextensions of L/F with degrees p and 2, respectively. Then we will study relations between the p-ranks of the class groups Cl(K) and Cl(k). 1. A Short History of Reflection Theorems Results comparing the p-rank of class groups of different number fields (often based on the interplay between Kummer theor...
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Let G = Dp be the dihedral group of order 2p, where p is an odd prime. Let k an algebraically closed field of characteristic p. We show that any action of G on the ring k[[y]] can be lifted to an action on R[[y]], where R is some complete discrete valuation ring with residue field k and fraction field of characteristic 0. 2000 Mathematics subject Classification. Primary 14H37. Secondary: 11G20,...
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This paper focuses on the following two questions relating to the inverse Galois problem: (1) (Beckmann [2]) Is every finite Galois extension of Q the specialization of a Galois branched covering of P defined over Q and with the same Galois group? (2) (Birch [3]) Given a finite group G, is there a tamely ramified normal extension F/Q with Gal(F/Q) ∼ = G? We obtain affirmative answers to these q...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1998
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7466