Abelian extensions of global fields with constant local degrees

Details Abelian extensions of global fields with constant local degrees Abelian extensions of global fields with constant local degrees

2004-12-08

arxiv.org/abs/math/0412176v4

Mathematics

Number Theory

7 pages. The present version gives a different proof of the main result. In the previous version, a special case was overlooke

Scientific paper

Given a global field K and a positive integer n, there exists an abelian
extension L/K (of exponent n) such that the local degree of L/K is equal to n
at every finite prime of K, and is equal to two at the real primes if n=2. As a
consequence, the n-torsion subgroup of the Brauer group of K is equal to the
relative Brauer group of L/K.

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