✦ LIBER ✦

An equivalence between local fields

✍ Scribed by Ilaria Del Corso; Roberto Dvornicich

Book ID: 104024531
Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 254 KB
Volume: 115
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2004.10.011

No coin nor oath required. For personal study only.

✦ Synopsis

The p-component of the index of a number field K depends only on the completions of K at the primes over p. In this paper we define an equivalence relation between m-tuples of local fields such that, if two number fields K and K have equivalent m-tuples of completions at the primes over p, then they have the same p-component of the index. This equivalence can be interpreted in terms of the decomposition groups of the primes over p of the normal closures of K and K .

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