On the Local Behavior of Specializations of Function Field Extensions. (28th February 2018) - König, Joachim; Legrand, François; Neftin, Danny
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 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.