On a conjecture of Mazur predicting the growth of Mordell--Weil ranks in ℤ_p-extensions

2024/01/15 by Gajek-Leonard, Rylan, Hatley, Jeffrey, Kundu, Debanjana +1
#11R23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.07792

Abstract

Let p be an odd prime. We study Mazur's conjecture on the growth of the Mordell--Weil ranks of an elliptic curve E/ℚ over ℤ_p-extensions of an imaginary quadratic field, where p is a prime of good reduction for E. In particular, we obtain criteria that may be checked through explicit calculation, thus allowing for the verification of Mazur's conjecture in specific examples.

Related

• Ranks of elliptic curves over Z_p²-extensions
• Mazur's Growth Number Conjecture in the Rank One Case
• Mazur's growth number conjecture and congruences
• On the Mordell-Weil Ranks of supersingular abelian varieties over\n \ℤ_p²-extensions
• Rankin-Selberg L-functions in cyclotomic towers, II