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October 8, 2025MathematikaOpen Access

The growth of Tate–Shafarevich groups of pp‐supersingular elliptic curves over anticyclotomic ZpZₚ‐extensions at inert primes

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The Mordell–Weil ranks are shown to be bounded over subextensions of the anticyclotomic Zp-extension.
An asymptotic formula for the growth of Tate–Shafarevich groups is provided for these elliptic curves.
The signed Selmer groups serve as cotorsion modules over the respective Iwasawa algebra.
This work examines elliptic curves with good supersingular reduction at inert primes in imaginary quadratic fields.

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Implication

This research demonstrates bounded Mordell–Weil ranks in elliptic curves over anticyclotomic Zp extensions, highlighting the role of signed Selmer groups.

Cite This Study

Işik et al. (2025) studied this question.

synapsesocial.com/papers/68e6f342f8145af55aeacb77 https://doi.org/10.1112/mtk.70050

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Implication

This research demonstrates bounded Mordell–Weil ranks in elliptic curves over anticyclotomic Zp extensions, highlighting the role of signed Selmer groups.

The growth of Tate–Shafarevich groups of pp‐supersingular elliptic curves over anticyclotomic ZpZₚ‐extensions at inert primes

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Discussion

Implication

Cite This Study

The growth of Tate–Shafarevich groups of pp‐supersingular elliptic curves over anticyclotomic ZpZₚ‐extensions at inert primes

Key Points

Discussion

Implication

Cite This Study

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