4 papers
On the local-global principle for twists of abelian varieties and Galois representations
Nirvana Coppola, Lorenzo La Porta, Matteo Longo
This paper investigates the validity of a local-global principle for finite twists of a large class of objects endowed with a continuous action of the absolute Galois group of a gi…
On anticyclotomic Selmer groups of elliptic curves
Matteo Longo, Jishnu Ray, Stefano Vigni
Let be a prime number and let be an imaginary quadratic field where is unramified. Under mild technical assumptions, in this paper we prove the non-existence of no…
A generalized Rubin formula for Hecke characters
Matteo Longo, Stefano Vigni, Shilun Wang
The goal of this paper is to generalize Rubin's theorem on values of Katz's -adic -function outside the range of interpolation from the case of Hecke characters of CM ellipti…
Kolyvagin's conjecture for modular forms
Matteo Longo, Maria Rosaria Pati, Stefano Vigni
Our main result in this article is a proof (under mild technical assumptions) of an analogue for -adic Galois representations attached to a newform of even weight o…