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Sbornik: Mathematics, 2021, Volume 212, Issue 3, Pages 274–287
DOI: https://doi.org/10.1070/SM9429 (Mi sm9429) 		 
Versal families of elliptic curves with rational 3-torsion

B. M. Bekkera, Yu. G. Zarhinb

a Faculty of Mathematics and Mechanics, Saint Petersburg State University, St. Petersburg, Russia
b Department of Mathematics, Pennsylvania State University, University Park, PA, USA
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DOI: https://doi.org/10.1070/SM9429
Abstract: For an arbitrary field of characteristic different from 2 and 3, we construct versal families of elliptic curves whose 3-torsion is either rational or isomorphic to $\mathbb Z/3\mathbb Z\oplus \mu_3$ as a Galois module.
Bibliography: 10 titles.
Keywords: elliptic curves, torsion points, Galois modules.
Funding agency Grant number
Simons Foundation 585711
Yu. G. Zarhin's research was carried out with the support of the Simons Foundation Collaboration (grant no. 585711).
Received: 22.04.2020
Russian version:
Matematicheskii Sbornik, 2021, Volume 212, Number 3, Pages 6–19
DOI: https://doi.org/10.4213/sm9429
Bibliographic databases:
Document Type: Article
UDC: 512.742.72
MSC: 11G05, 14H52
Language: English
Original paper language: Russian
Citation: B. M. Bekker, Yu. G. Zarhin, “Versal families of elliptic curves with rational 3-torsion”, Sb. Math., 212:3 (2021), 274–287
Citation in format AMSBIB
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\by B.~M.~Bekker, Yu.~G.~Zarhin
\paper Versal families of elliptic curves with rational 3-torsion
\jour Sb. Math.
\yr 2021
\vol 212
\issue 3
\pages 274--287
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