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

V. I. Nesteruk


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.


Pseudolocal field, $n$-dimensional pseudolocal field, $n$-dimensional general local field, isogeny, Tate pairing associated to an isogeny, local Artin map, Hilbert symbol, Kolyvagin's formula

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