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Arbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varieties

Abstract:
We show that, for any d, the 2-torsion of Tate-Shafarevich groups of absolutely simple abelian varieties of dimension d over 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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4064 / aa171118-7-12

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
New College
Role:
Author
ORCID:
0000-0002-3340-8868
Publisher:
Polskiej Akademii Nauk
Journal:
Acta Arithmetica More from this journal
Volume:
191
Pages:
101-114
Publication date:
2019-09-05
Acceptance date:
2018-12-05
DOI:
EISSN:
1730-6264
ISSN:
0065-1036
Keywords:
Pubs id:
pubs:950989
UUID:
uuid:22383ccd-250e-4c3b-a4a7-62a995e01a1b
Local pid:
pubs:950989
Source identifiers:
950989
Deposit date:
2018-12-07

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