Regulators of Elliptic Curves
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Regulators of Elliptic Curves. / Autissier, Pascal; Hindry, Marc; Pazuki, Fabien.
In: International Mathematics Research Notices, Vol. 2021, No. 7, 2021, p. 4976–4993.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Regulators of Elliptic Curves
AU - Autissier, Pascal
AU - Hindry, Marc
AU - Pazuki, Fabien
PY - 2021
Y1 - 2021
N2 - We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic p>0. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field. In the function field case, we obtain that non-trivial families of elliptic curves with bounded regulators and bounded ranks are limited families. We conclude by asking new questions.
AB - We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic p>0. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field. In the function field case, we obtain that non-trivial families of elliptic curves with bounded regulators and bounded ranks are limited families. We conclude by asking new questions.
U2 - 10.1093/imrn/rny285
DO - 10.1093/imrn/rny285
M3 - Journal article
VL - 2021
SP - 4976
EP - 4993
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 7
ER -
ID: 215085178