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math.NT2022
Large rank jumps on elliptic surfaces and the Hilbert property
Renato Dias Costa, Cecília Salgado
Given a rational elliptic surface over a number field, we study the collection of fibers whose Mordell--Weil rank is greater than the generic rank. We give conditions on the singul…
math.NT2019
Rank jumps on elliptic surfaces and the Hilbert property
Daniel Loughran, Cecília Salgado
Given an elliptic surface over a number field, we study the collection of fibres whose Mordell-Weil rank is greater than the generic rank. Under suitable assumptions, we show that…