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Regulators of number fields and abelian varieties

Date: Thursday, January 23, 2020 13:30 - 15:30
Speaker: Fabien Pazuki (University of Copenhagen)
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Tim Browning

In the general study of regulators, we present three inequalities, and some corollaries about the Northcott property and about a counting problem for rational points on elliptic curves. We first bound from below the regulators of number fields, following previous works of Silverman and Friedman. We then bound from below the regulators of Mordell-Weil groups of abelian varieties defined over a number field, assuming a conjecture of Lang and Silverman. Finally we explain how to prove an unconditional statement for elliptic curves of rank at least 4. This third inequality is joint work with Pascal Autissier and Marc Hindry.
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