scholarly journals On a norm property of Hilbert symbol over polynomial formal module in multidimensional local field

2016 ◽  
Vol 3(61) (4) ◽  
pp. 552-557
Author(s):  
Vladislav V. Volkov ◽  
Keyword(s):  
Local Field ◽  
Hilbert Symbol ◽  
Formal Module ◽  
Norm Property

scholarly journals On the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol

2013 ◽  
Vol 5 (1) ◽  
pp. 94-101
Author(s):  
V.I. Nesteruk
Keyword(s):  
Elliptic Curves ◽  
Local Field ◽  
Abelian Varieties ◽  
Tate Pairing ◽  
Hilbert Symbol

A proof of nondegeneracy of the Tate pairing and Kolyvagin's formula for elliptic curves with good reductions over an $n$-dimensional $(n\leq 3)$ pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal field and an $n$-dimensional $(n\leq 3)$ pseudolocal field, and the relations of local Artin map and of the Hilbert symbol for an $n$-dimensional $(n\leq 3)$ general local field is given.

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