Open AccessOn the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol
Author(s) -
V. I. Nesteruk
Publication year - 2013
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.5.1.94-101
Subject(s) - isogeny , mathematics , pairing , abelian group , field (mathematics) , symbol (formal) , pure mathematics , elliptic curve , condensed matter physics , physics , superconductivity , computer science , programming language
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.