✦ LIBER ✦

Norm Groups of Global Fields

✍ Scribed by K. Hutchinson

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 184 KB
Volume: 50
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1026

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✦ Synopsis

Leonid Stern (1989. J. Number Theory 32, 203-219; 1990, J. Number Theory 36. 127-132) proves that two finite Galois extensions of a global field are equal if the images of the norm maps are equal and that, for a nontrivial finite separable extension of global fields, the image of the norm has infinite index. In this note we show that these results follow easily from Tchebotarev density. We do this by first proving the results for the images of the norm map on divisors and then by showing that if the images of the norm maps of two extensions are almost equal then the corresponding images of the divisor norm maps are almost equal also.

' 1995 Academic Press. Inc.

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