On the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts 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.
1998 ◽
Vol 126
(10)
◽
pp. 2855-2856
2016 ◽
Vol 102
(3)
◽
pp. 316-330
◽
2019 ◽
Vol 15
(03)
◽
pp. 569-584
Keyword(s):
1998 ◽
Vol 64
(2)
◽
pp. 178-194
◽
2016 ◽
Vol 12
(02)
◽
pp. 445-463
◽
Keyword(s):
1970 ◽
Vol 12
(3)
◽
pp. 477-488
◽