Add to ORKGAbstract: Let K be a CM field and O be its ring of integers. Let p be an odd prime integer and p be a prime in K lying above p. Let F be a Galois extension of K unramified over p. For an Abelian variety A defined over F with complex multiplication by O, we study the variation of the p-ranks of the Selmer groups in pro-p algebraic extensions. We first study the Zp-extension case. When K is quadratic imaginary and E is an elliptic curve, we also study the p-ranks of the Selmer groups in an unramified p-class field tower. 1
17 pages; final version, to appear in Compositio MathematicaInternational audienceLet $A$ be an abel...
This work generalizes the theory of arithmetic local constants, introduced by Mazur and Rubin, to be...
Let A/Q be a modular abelian variety attached to a weight 2 new modular form of level N=pM, where p ...
We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields...
Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let ...
AbstractLet p be an odd prime, and let K/K0 be a quadratic extension of number fields. Denote by K± ...
Let p be an odd prime, and let K/K0 be a quadratic extension of number fields. Denote by K ± the max...
19 pages; final version, to appear in Journal of the London Mathematical SocietyInternational audien...
It is known that, for every elliptic curve over ℚ, there exists a quadratic extension in which the r...
It is known that, for every elliptic curve over ℚ, there exists a quadratic extension in which the r...
© 2015 The Author(s). Let A be an abelian variety defined over a number field k and F a finite Galoi...
Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let ...
Let $E$ be an elliptic curve defined over a number field $F$ with good ordinary reduction at all pri...
Thesis (Ph. D.)--University of Washington, 2003The Mordell-Weil theorem states that the points of an...
Let $F$ be a number field unramified at an odd prime $p$ and $F_\infty$ be the $\mathbf{Z}_p$-cyclot...
17 pages; final version, to appear in Compositio MathematicaInternational audienceLet $A$ be an abel...
This work generalizes the theory of arithmetic local constants, introduced by Mazur and Rubin, to be...
Let A/Q be a modular abelian variety attached to a weight 2 new modular form of level N=pM, where p ...
We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields...
Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let ...
AbstractLet p be an odd prime, and let K/K0 be a quadratic extension of number fields. Denote by K± ...
Let p be an odd prime, and let K/K0 be a quadratic extension of number fields. Denote by K ± the max...
19 pages; final version, to appear in Journal of the London Mathematical SocietyInternational audien...
It is known that, for every elliptic curve over ℚ, there exists a quadratic extension in which the r...
It is known that, for every elliptic curve over ℚ, there exists a quadratic extension in which the r...
© 2015 The Author(s). Let A be an abelian variety defined over a number field k and F a finite Galoi...
Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let ...
Let $E$ be an elliptic curve defined over a number field $F$ with good ordinary reduction at all pri...
Thesis (Ph. D.)--University of Washington, 2003The Mordell-Weil theorem states that the points of an...
Let $F$ be a number field unramified at an odd prime $p$ and $F_\infty$ be the $\mathbf{Z}_p$-cyclot...
17 pages; final version, to appear in Compositio MathematicaInternational audienceLet $A$ be an abel...
This work generalizes the theory of arithmetic local constants, introduced by Mazur and Rubin, to be...
Let A/Q be a modular abelian variety attached to a weight 2 new modular form of level N=pM, where p ...