Premium
Solving embedding problems with bounded ramification
Author(s) -
Jarden Moshe,
Ramiharimanantsoina Cynthia
Publication year - 2018
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12126
Subject(s) - ramification , mathematics , embedding , bounded function , pure mathematics , artificial intelligence , mathematical analysis , computer science
Let K / K 0be a finite Galois extension of global fields. We prove that every finite embedding problem with a solvable kernel H for K / K 0is solvable if it is locally solvable and satisfies two conditions onchar ( K 0 ) and the roots of unity in K . Moreover, the solution can be chosen to coincide with finitely many (given in advance) local solutions. Finally, and this is the main point of this work, the number of primes of K 0 that ramify in the solution field is bounded by the number of primes of K 0 that ramify in K plus the number of prime divisors of | H | , counted with multiplicity.