scholarly journals p-adic height pairings on abelian varieties with semistable ordinary reduction

2003 ◽  
Vol 2003 (564) ◽  
Author(s):  
Adrian Iovita ◽  
Annette Werner
Keyword(s):  
Abelian Varieties ◽  
Ordinary Reduction

Bounding the Iwasawa invariants of Selmer groups

2020 ◽  
pp. 1-33
Author(s):  
Sören Kleine
Keyword(s):  
Number Field ◽  
Analogous Result ◽  
Abelian Varieties ◽  
Fixed Number ◽  
Selmer Groups ◽  
Iwasawa Invariants ◽  
Ordinary Reduction

Abstract We study the growth of p-primary Selmer groups of abelian varieties with good ordinary reduction at p in ${{Z}}_p$ -extensions of a fixed number field K. Proving that in many situations the knowledge of the Selmer groups in a sufficiently large number of finite layers of a ${{Z}}_p$ -extension over K suffices for bounding the over-all growth, we relate the Iwasawa invariants of Selmer groups in different ${{Z}}_p$ -extensions of K. As applications, we bound the growth of Mordell–Weil ranks and the growth of Tate-Shafarevich groups. Finally, we derive an analogous result on the growth of fine Selmer groups.

scholarly journals Classification of nonrigid families of abelian varieties

1993 ◽  
Vol 45 (2) ◽  
pp. 159-189
Author(s):  
Masa-Hiko Saitō
Keyword(s):  
Abelian Varieties
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