Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion |
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| Authors: | Sara Arias‐de‐Reyna Wojciech Gajda Sebastian Petersen |
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| Affiliation: | 1. Mathematics Research Unit, University of Luxembourg, L‐1359 Luxembourg. Phone: +352 46 66 44 6269;2. Department of Mathematics, Adam Mickiewicz University, 61614 Poznań, Poland. Phone: +48 61 829 5503;3. Fachbereich Mathematik, Universit?t Kassel, 34132 Kassel, Germany |
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| Abstract: | In this paper we prove the Geyer‐Jarden conjecture on the torsion part of the Mordell‐Weil group for a large class of abelian varieties defined over finitely generated fields of arbitrary characteristic. The class consists of all abelian varieties with big monodromy, i.e., such that the image of Galois representation on ?‐torsion points, for almost all primes ?, contains the full symplectic group. |
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| Keywords: | Abelian variety Galois representation Haar measure MSC (2010) 11E30 11G10 14K15 |
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