Division by 2 on odd-degree hyperelliptic curves and their Jacobians
- Autores: Zarhin Y.G.1
-
Afiliações:
- Department of Mathematics, Pennsylvania State University
- Edição: Volume 83, Nº 3 (2019)
- Páginas: 93-112
- Seção: Articles
- URL: https://journal-vniispk.ru/1607-0046/article/view/133775
- DOI: https://doi.org/10.4213/im8773
- ID: 133775
Citar
Resumo
Palavras-chave
Sobre autores
Yuri Zarhin
Department of Mathematics, Pennsylvania State University
Email: zarhin@math.psu.edu
Doctor of physico-mathematical sciences, Professor
Bibliografia
- Д. Мамфорд, Лекции о тета-функциях, Мир, М., 1988, 448 с.
- L. C. Washington, Elliptic curves. Number theory and cryptography, Discrete Math. Appl. (Boca Raton), 2nd ed., Chapman & Hall/CRC, Boca Raton, FL, 2008, xviii+513 pp.
- M. Stoll, “Chabauty without the Mordell–Weil group”, Algorithmic and experimental methods in algebra, geometry, and number theory, Springer, Cham, 2017, 623–663
- Б. М. Беккер, Ю. Г. Зархин, “Деление на $2$ рациональных точек на эллиптических кривых”, Алгебра и анализ, 29:4 (2017), 196–239
- E. F. Schaefer, “$2$-descent on the Jacobians of hyperelliptic curves”, J. Number Theory, 51:2 (1995), 219–232
- J. Yelton, “Images of $2$-adic representations associated to hyperelliptic Jacobians”, J. Number Theory, 151 (2015), 7–17
- M. Stoll, Arithmetic of hyperelliptic curves, Summer semester 2014, Univ. of Bayreuth, 2014, 42 pp.
- J. Boxall, D. Grant, “Examples of torsion points on genus two curves”, Trans. Amer. Math. Soc., 352:10 (2000), 4533–4555
- Ж. Серр, Алгебраические группы и поля классов, Мир, М., 1968, 285 с.
- N. Bruin, E. V. Flynn, “Towers of $2$-covers of hyperelliptic curves”, Trans. Amer. Math. Soc., 357:11 (2005), 4329–4347
- J. Boxall, D. Grant, F. Leprevost, “$5$-torsion points on curves of genus $2$”, J. London Math. Soc. (2), 64:1 (2001), 29–43
- M. Raynaud, “Courbes sur une variete abelienne et points de torsion”, Invent. Math., 71:1 (1983), 207–233
- B. Poonen, M. Stoll, “Most odd degree hyperelliptic curves have only one rational point”, Ann. of Math. (2), 180:3 (2014), 1137–1166
- M. Raynaud, “Sous-varietes d'une variete abelienne et points de torsion”, Arithmetic and geometry, Papers dedicated to I. R. Shafarevich on the occasion of his sixtieth birthday, v. I, Progr. Math., 35, Birkhäuser Boston, Boston, MA, 1983, 327–352
Arquivos suplementares
