The regulator dominates the rank

2022/01/07 by Fabien Pazuki, Pazuki, Fabien
Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2201.02383

Abstract

After noticing that the regulator of a number field dominates the rank of its group of units, we bound from below the regulator of the Mordell-Weil group of elliptic curves over global function fields of characteristic p≥5. The lower bound is an increasing function of the rank and of the height.

Related

• Hodge theory and the Mordell-Weil rank of elliptic curves over extensions of function fields
• Elliptic curves with bounded ranks in function field towers
• Root numbers and ranks in positive characteristic
• Mordell-Weil groups and the rank of elliptic curves over large fields
• Heights, ranks and regulators of abelian varieties