What type of study is this?

This is a Quantitative Study study.

September 29, 2025Open Access

Mazur's growth number conjecture and congruences

View Full Paper

Ask AI

Bookmark

Establishing Mazur's conjecture for specific triples demonstrates significant connections between growth of Selmer ranks and Galois representations.
The findings show that the Mordell-Weil ranks in certain extensions remain bounded for elliptic curves, suggesting parallels with modular forms.
Results further indicate that congruences mod p play a crucial role in linking Selmer ranks and Galois representations.
This work builds on and extends existing results related to Greenberg-Vatsal and Emerton-Pollack-Weston, providing new insights into the conjecture.

No takes yet. Share an insight, caveat, or question.

The exploration reveals how Mazur's conjecture on Selmer ranks applies under Galois representations, suggesting bounded Mordell-Weil ranks.

Anwesh Ray (2025) studied this question.

View Full Paper

Ask AI

Bookmark

The exploration reveals how Mazur's conjecture on Selmer ranks applies under Galois representations, suggesting bounded Mordell-Weil ranks.