Geodesic
Arbitrarily large 2-torsion in Tate–Shafarevich groups of abelian varieties
E. V. Flynn1
1 Mathematical Institute University of Oxford Andrew Wiles Building Radcliffe Observatory Quarter, Woodstock Road Oxford OX2 6GG United Kingdom
Acta Arithmetica, Tome 191 (2019) no. 2, pp. 101-114 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that, for any $d$, the $2$-torsion of Tate–Shafarevich groups of absolutely simple abelian varieties of dimension $d$ over $\mathbb Q $ can be arbitrarily large. This involves the use of an approach, which we shall describe, for demonstrating arbitrarily large Tate–Shafarevich groups which does not require entire Selmer groups to be found.
DOI : 10.4064/aa171118-7-12
Keywords: nbsp torsion tate shafarevich groups absolutely simple abelian varieties dimension nbsp nbsp mathbb arbitrarily large involves approach which shall describe demonstrating arbitrarily large tate shafarevich groups which does require entire selmer groups found

E. V. Flynn 1

1 Mathematical Institute University of Oxford Andrew Wiles Building Radcliffe Observatory Quarter, Woodstock Road Oxford OX2 6GG United Kingdom 
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     title = {Arbitrarily large 2-torsion in {Tate{\textendash}Shafarevich} groups of abelian varieties},
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E. V. Flynn. Arbitrarily large 2-torsion in Tate–Shafarevich groups of abelian varieties. Acta Arithmetica, Tome 191 (2019) no. 2, pp. 101-114. doi: 10.4064/aa171118-7-12

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