Type: Other
Publication Date: 2022-01-01
Citations: 0
DOI: https://doi.org/10.1090/conm/779/15674
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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p greater-than-or-equal-to 5"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>5</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">p\geq 5</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The lower bound is an increasing function of the rank and of the height. This partially answers Question 7.1 and Question 7.2 in Autissier et al [Int. Math. Res. Not., 7, 2021, 4976-4993].
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