Rational separability of the integral closure

We investigate the following question. Let K be a global field, i.e. a number field or an algebraic function field of one variable over a finite field of constants. Let W K be a set of primes of K, possibly infinite, such that in some fixed finite separable extension L of K, all the primes of W K do...

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Bibliographic Details
Published in:Journal of number theory 2009-10, Vol.129 (10), p.2227-2259
Main Author: Shlapentokh, Alexandra
Format: Article
Language:English
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Summary:We investigate the following question. Let K be a global field, i.e. a number field or an algebraic function field of one variable over a finite field of constants. Let W K be a set of primes of K, possibly infinite, such that in some fixed finite separable extension L of K, all the primes of W K do not have factors of relative degree 1. Let M be a finite extension of K and let W M be the set of all the M-primes above the primes of W K . Then does W M have the same property? The answer is “always” for one variable algebraic function fields over finite fields of constants and “not always” for number fields. In this paper we give a complete description of the conditions under which W M inherits and does not inherit the above described property.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2009.05.002