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 infini
On the norm groups of global fields
โ Scribed by Leonid Stern
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 802 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let Lรk and Tรk be finite extensions of algebraic number fields. In the present work we introduce the factor group of k\* & N Lรk J L N Tรk J T by (k\* & N Tรk J T ) N Lรk L\*, where J L and J T are the idele groups of L and T, respectively. The main theorem shows that the computation of this factor
We examine the Mazur-Tate canonical height pairing defined between an abelian variety over a global field and its dual. We show in the case of global function fields that certain of these pairings are annihilated by universal norms coming from Carlitz cyclotomic extensions. Furthermore, for elliptic
We prove that any finite abelian group is the ideal class group of the ring of S-integers of some global field of given characteristic. ## 1999 Academic Press Nous prouvons que tout groupe abe lien fini est groupe des classes d'ide aux de l'anneau des S-entiers d'un corps global de caracte ristiqu
Let K be a finite extension of Q p and F (X, Y ) be a formal group defined over O K where O K is the ring of integers of K. For an arbitrary Z p -extensions K โ /K and the nth layer K n , we study the index [F (K n-1 ) : We give the asymptotic behavior of the index as n โ โ, and determine the index