19 citations · 24 across the 3 of their papers we have counts for
5 papers
Quaternionic Darmon points on p-adic tori and abelian varieties
M. Longo, S. Vigni
We prove formulas for the p-adic logarithm of quaternionic Darmon points on p-adic tori and modular abelian varieties over Q having purely multiplicative reduction at p. These form…
The rationality of quaternionic Darmon points over genus fields of real quadratic fields
M. Longo, S. Vigni
Darmon points on p-adic tori and Jacobians of Shimura curves over Q were introduced in previous joint works with Rotger as generalizations of Darmon's Stark-Heegner points. In this…
On the vanishing of Selmer groups for elliptic curves over ring class fields
M. Longo, S. Vigni
Let E be a rational elliptic curve of conductor N without complex multiplication and let K be an imaginary quadratic field of discriminant D prime to N. Assume that the number of p…
Torsion points on elliptic curves over function fields and a theorem of Igusa
A. Bandini, I. Longhi, S. Vigni
If F is a global function field of characteristic p>3, we employ Tate's theory of analytic uniformization to give an alternative proof of a theorem of Igusa describing the image of…
On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields
S. Vigni
If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to…