9 citations · 17 across the 7 of their papers we have counts for
7 papers
On the structure of elliptic curves over finite extensions of with additive reduction
Michiel Kosters, René Pannekoek
Let be a prime and let be a finite extension of . Let be an elliptic curve with additive reduction. In this paper, we study the topological group struct…
Diophantus Revisited: On rational surfaces and K3 surfaces in the Arithmetica
René Pannekoek
This article wants to show two things: first, that certain problems in Diophantus' Arithmetica lead to equations defining del Pezzo surfaces or other rational surfaces, while certa…
Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields
Lisa Berger, Chris Hall, René Pannekoek +5
We study the Jacobian of the smooth projective curve of genus with affine model over the function field , when is p…
The Brauer-Manin obstruction on Kummer varieties and ranks of twists of abelian varieties
David Holmes, René Pannekoek
Let r > 0 be an integer. We present a sufficient condition for an abelian variety A over a number field k to have infinitely many quadratic twists of rank at least r, in terms of d…
On p-adic density of rational points on K3 surfaces
René Pannekoek
We show that, for every prime number p, there exist infinitely many K3 surfaces over Q whose rational points lie dense in the space of p-adic points. We also show that there exists…
On p-torsion of p-adic elliptic curves with additive reduction
René Pannekoek
Let E be an elliptic curve with additive reduction over the p-adic numbers, and let G be the group of p-adic points on E that have good reduction. This paper gives necessary and su…