On the Local Behavior of Specializations of Function Field Extensions. (28th February 2018)

• Record Type: Journal Article
• Authors: König, Joachim; Legrand, François; Neftin, Danny
• Is Part Of: International mathematics research notices. Volume 2019:Number 9(2019)
• Page Start: 2951
• Page End: 2980
• Publication Date: 2018-02-28
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rny016
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: Given a field k of characteristic zero and an indeterminate T over k, we investigate the local behavior at primes of k of finite Galois extensions of k arising as specializations of finite Galois extensions E / k ( T ) (with E / k regular) at points $t_{0} \in \mathbb{P}^{1}(k)$ . We provide a general result about decomposition groups at primes of k in specializations, extending a fundamental result of Beckmann concerning inertia groups. We then apply our result to study crossed products, the Hilbert-Grunwald property, and finite parametric sets.