✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.