1 results
Bounding the Iwasawa invariants of Selmer groups
- Part of
-
- Journal:
- Canadian Journal of Mathematics / Volume 73 / Issue 5 / October 2021
- Published online by Cambridge University Press:
- 29 June 2020, pp. 1390-1422
- Print publication:
- October 2021
-
- Article
- Export citation
-
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.
