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45 papers · 1 filter
On the structure of the Bloch--Kato Selmer groups of modular forms over anticyclotomic -towers
Antonio Lei, Luca Mastella, Luochen Zhao
Let be an odd prime number and let be an imaginary quadratic field in which is split. Let be a modular form with good reduction at . We study the variation of th…
On simultaneous approximation to a real number, its square, and its cube, II
Damien Roy
In a previous paper with the same title, we gave an upper bound for the exponent of uniform rational approximation to a quadruple of -linearly independent real numbers…
On a conjecture of Mazur predicting the growth of Mordell--Weil ranks in -extensions
Rylan Gajek-Leonard, Jeffrey Hatley, Debanjana Kundu +1
Let be an odd prime. We study Mazur's conjecture on the growth of the Mordell--Weil ranks of an elliptic curve over -extensions of an imaginary qua…
Algebraic structure and characteristic ideals of fine Mordell--Weil groups and plus/minus Mordell--Weil groups
Antonio Lei
Given an elliptic curve defined over a number field , we study the algebraic structure and prove a control theorem for Wuthrich's fine Mordell--Weil groups over a …
A remark on the characteristic elements of anticyclotomic Selmer groups of elliptic curves with complex multiplication at supersingular primes
Antonio Lei
Let be a prime number. Let be an elliptic curve with complex multiplication by an imaginary quadratic field such that is inert in and that ha…
Exponents of Diophantine approximation in dimension two for a general class of numbers
Anthony Poëls
We study the Diophantine properties of a new class of transcendental real numbers which contains, among others, Roy's extremal numbers, Bugeaud-Laurent Sturmian continued fractions…