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홈 > 학술정보 >학술행사 > 세미나
한국고등과학원 Number Theory Seminar

Title
On specializations of regular Galois extensions over number fields
Speaker
Keonig, Joachim   (Technion, Israel )
Date
2017-02-23 17:00:00
Host
KIAS
Place
1424
Abstract
For a number field K, we investigate the set of specializations of a regular Galois extension E|K(t) with Galois group G, and its relation to some classical problems. The Beckmann-Black Problem asks whether every G-extension of K arises as a specialization of some such E|K(t). We use a notion of 'parametric sets' of regular Galois extensions to provide negative answers to more restrictive versions of the Beckmann-Black Problem. The Grunwald Problem asks whether, for given local extensions (all with Galois group embedding into G) at finitely many primes of K, there always exists a G-extension of K which approximates all these local extensions. We investigate to what extent the specializations of some given regular Galois extensions can provide positive answers to this question. (The first part is joint work with Francois Legrand. The second part is joint work in progress with Francois Legrand and Danny Neftin.)
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