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

V. I. Nesteruk | Zendy

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On 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 -

carpathian mathematical publications

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 , local field , combinatorics , geometry , physics , superconductivity , computer science , programming language , quantum mechanics

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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