Unramified alternating extensions of quadratic fields

2001/03/30 by Kiran S. Kedlaya, Kedlaya, Kiran S.
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #math.NT #msc:11S05 #msc:11S15 #msc:12F05

paper · pdf · doi:10.48550/arxiv.math/0103234

4 pages

arxiv created 2001/03/30 · arxiv updated 2009/11/30

Abstract

We exhibit, for n at least 5, infinitely many quadratic number fields admitting unramified degree n extensions with prescribed signature whose normal closures have Galois group A_n. This generalizes a result of Uchida and Yamamoto, which did not include the ability to restrict the signature, and a result of Yamamura, which was the case n=5.

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