The growth of Tate–Shafarevich groups in cyclic extensions

DOI10.1112/S0010437X22007734OpenAlexW4308215216MaRDI QIDQ5052199

Yi Ouyang, Jian-Feng Xie

Publication date: 22 November 2022

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0010437x22007734

zbMATH Keywords

abelian varietiesSelmer groupsTate-Shafarevich groupsfine Tate-Shafarevich groupstwist of abelian varieties

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Abelian varieties of dimension (> 1) (11G10) Arithmetic ground fields for abelian varieties (14K15) Algebraic theory of abelian varieties (14K05) Galois cohomology (11R34)

Cites Work

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• Twisting commutative algebraic groups
• Finding large Selmer rank via an arithmetic theory of local constants
• The fine Tate–Shafarevich group
• Diophantine stability
• Class Field Theory
• Selmer groups as flat cohomology groups
• The growth of fine Selmer groups
• Selmer groups and class groups
• p-Selmer growth in extensions of degree p
• Class groups of global fields.
• On the arithmetic of abelian varieties

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