On the Kolyvagin’s formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol - Nesteruk, V.I. (Carpathian Mathematical Publications, 2013)
A proof of nondegeneracy of the Tate pairing and Kolyvagin's formula for elliptic curves with good reductions over an n-dimensional (n≤ 3) pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal field and an n-dimensional (n≤ 3) pseudolocal field, and the relations of local Artin map and of the Hilbert symbol for an n-dimensional (n≤ 3) general local field is given.