TY - JOUR
T1 - ARBITRARILY LARGE p-TORSION IN TATE-SHAFAREVICH GROUPS
AU - Victor Flynn, E.
AU - Shnidman, Ari
AU - Fisher, Tom
N1 - Publisher Copyright:
© 2024 The Author(s).
PY - 2025/3/1
Y1 - 2025/3/1
N2 - We show that, for any prime p, there exist absolutely simple abelian varieties over with arbitrarily large p-torsion in their Tate-Shafarevich groups. To prove this, we construct explicit -covers of Jacobians of curves of the form which violate the Hasse principle. In the appendix, Tom Fisher explains how to interpret our proof in terms of a Cassels-Tate pairing.
AB - We show that, for any prime p, there exist absolutely simple abelian varieties over with arbitrarily large p-torsion in their Tate-Shafarevich groups. To prove this, we construct explicit -covers of Jacobians of curves of the form which violate the Hasse principle. In the appendix, Tom Fisher explains how to interpret our proof in terms of a Cassels-Tate pairing.
KW - Tate-Shafarevich group
KW - abelian variety
UR - https://www.scopus.com/pages/publications/85210382862
U2 - 10.1017/S1474748024000392
DO - 10.1017/S1474748024000392
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AN - SCOPUS:85210382862
SN - 1474-7480
VL - 24
SP - 481
EP - 502
JO - Journal of the Institute of Mathematics of Jussieu
JF - Journal of the Institute of Mathematics of Jussieu
IS - 2
ER -