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 ($nleq 3$) pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal field and an $n$-dimensional ($nleq 3$) pseudo...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2013-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/166/132 |
| _version_ | 1828529423621554176 |
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| author | V. I. Nesteruk |
| author_facet | V. I. Nesteruk |
| author_sort | V. I. Nesteruk |
| collection | DOAJ |
| description | A proof of nondegeneracy of the Tate pairing and Kolyvagin's formula for elliptic curves with good reductions over an $n$-dimensional ($nleq 3$) pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal field and an $n$-dimensional ($nleq 3$) pseudolocal field, and the relations of local Artin map and of the Hilbert symbol for an $n$-dimensional ($nleq 3$) general local field isgiven. |
| first_indexed | 2024-12-11T22:08:42Z |
| format | Article |
| id | doaj.art-cdd222df8aa940fea573a1db86d3ce4c |
| institution | Directory Open Access Journal |
| issn | 2075-9827 |
| language | English |
| last_indexed | 2024-12-11T22:08:42Z |
| publishDate | 2013-06-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-cdd222df8aa940fea573a1db86d3ce4c2022-12-22T00:48:53ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272013-06-015194101On the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbolV. I. NesterukA proof of nondegeneracy of the Tate pairing and Kolyvagin's formula for elliptic curves with good reductions over an $n$-dimensional ($nleq 3$) pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal field and an $n$-dimensional ($nleq 3$) pseudolocal field, and the relations of local Artin map and of the Hilbert symbol for an $n$-dimensional ($nleq 3$) general local field isgiven.http://journals.pu.if.ua/index.php/cmp/article/view/166/132Pseudolocal fieldn-dimensional pseudolocal fieldn-dimensional general local fieldisogenyTate pairing associated to an isogenylocal Artin mapHilbert symbolKolyvagin's formula |
| spellingShingle | V. I. Nesteruk On the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol Karpatsʹkì Matematičnì Publìkacìï 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 |
| title | On the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol |
| title_full | On the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol |
| title_fullStr | On the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol |
| title_full_unstemmed | On the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol |
| title_short | On the Kolyvagin's formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol |
| title_sort | on the kolyvagin s formula the tate pairing associated to an isogeny the local artin map and the hilberts symbol |
| topic | 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 |
| url | http://journals.pu.if.ua/index.php/cmp/article/view/166/132 |
| work_keys_str_mv | AT vinesteruk onthekolyvaginsformulathetatepairingassociatedtoanisogenythelocalartinmapandthehilbertssymbol |