Add to ORKGLet p be an odd prime, and let K/K0 be a quadratic extension of number fields. Denote by K ± the maximal Zp-power extensions of K that are Galois over K0, with K+ abelian over K0 and K − dihedral over K0. In this paper we show that for a Galois representation over K0 satisfying certain hypotheses, if it has odd Selmer rank over K then for one of K ± its Selmer rank over L is bounded below by [L: K] for L ranging over the finite subextensions of K in K±. Our method of proof generalizes a method of Mazur–Rubin, building upon results of Nekovář, and applies to abelian varieties of arbitrary dimension, (self-dual twists of) modular forms of even weight, and (twisted
For an abelian variety A over a number field K, a consequence of the Birch and Swinnerton-Dyer conje...
Let p be a prime number and M a quadratic number field, M not equal Q(root p) if p equivalent to 1 m...
Let p be a prime number and M a quadratic number field, M ≠ ℚ() if p ≡ 1 mod 4. We will prove that f...
AbstractLet p be an odd prime, and let K/K0 be a quadratic extension of number fields. Denote by K± ...
AbstractLet p be an odd prime, and let K/K0 be a quadratic extension of number fields. Denote by K± ...
We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields...
Abstract: Let K be a CM field and O be its ring of integers. Let p be an odd prime integer and p be ...
Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let ...
Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let ...
© 2015 The Author(s). Let A be an abelian variety defined over a number field k and F a finite Galoi...
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...
AbstractWe give a new, somewhat elementary method for proving parity results about Iwasawa-theoretic...
A result due to R. Greenberg gives a relation between the cardinality of Selmer groups of elliptic c...
For an abelian variety A over a number field K, a consequence of the Birch and Swinnerton-Dyer conje...
For an abelian variety A over a number field K, a consequence of the Birch and Swinnerton-Dyer conje...
Let p be a prime number and M a quadratic number field, M not equal Q(root p) if p equivalent to 1 m...
Let p be a prime number and M a quadratic number field, M ≠ ℚ() if p ≡ 1 mod 4. We will prove that f...
AbstractLet p be an odd prime, and let K/K0 be a quadratic extension of number fields. Denote by K± ...
AbstractLet p be an odd prime, and let K/K0 be a quadratic extension of number fields. Denote by K± ...
We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields...
Abstract: Let K be a CM field and O be its ring of integers. Let p be an odd prime integer and p be ...
Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let ...
Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let ...
© 2015 The Author(s). Let A be an abelian variety defined over a number field k and F a finite Galoi...
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...
AbstractWe give a new, somewhat elementary method for proving parity results about Iwasawa-theoretic...
A result due to R. Greenberg gives a relation between the cardinality of Selmer groups of elliptic c...
For an abelian variety A over a number field K, a consequence of the Birch and Swinnerton-Dyer conje...
For an abelian variety A over a number field K, a consequence of the Birch and Swinnerton-Dyer conje...
Let p be a prime number and M a quadratic number field, M not equal Q(root p) if p equivalent to 1 m...
Let p be a prime number and M a quadratic number field, M ≠ ℚ() if p ≡ 1 mod 4. We will prove that f...