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Higher Degree Hilbert Symbol Equivalence of Algebraic Number Fields, II

✍ Scribed by Alfred Czogała; Andrzej Sładek


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
278 KB
Volume
72
Category
Article
ISSN
0022-314X

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✦ Synopsis


Hilbert symbol equivalence of degree n between two global fields containing a primitive n th root of unity is an isomorphism between the groups of n th power classes of these fields preserving Hilbert symbols of degree n. In the paper we prove that if n is an odd prime number then two number fields are Hilbert equivalent if and only if there exists a bijection between the sets of n-adic primes of the two fields which preserves the local degrees. This generalizes the known result for n=2.