179 citations · 759 across the 49 of their papers we have counts for
5 papers · 1 filter
Descent on elliptic curves
Michael Stoll
Let E be an elliptic curve over Q (or, more generally, a number field). Then on the one hand, we have the finitely generated abelian group E(Q), on the other hand, there is the Sha…
Finite descent obstructions and rational points on curves
Michael Stoll
Let k be a number field and X a smooth projective k-variety. In this paper, we study the information obtainable from descent via torsors under finite k-group schemes on the locatio…
Deciding existence of rational points on curves: an experiment
Nils Bruin, Michael Stoll
We consider all genus 2 curves over Q given by an equation y^2 = f(x) with f a squarefree polynomial of degree 5 or 6, with integral coefficients of absolute value at most 3. For e…
On the number of rational squares at fixed distance from a fifth power
Michael Stoll
The main result of this note is that there are at most seven rational points (including the one at infinity) on the curve C_A with the affine equation y^2 = x^5 + A (where A is a t…
Independence of rational points on twists of a given curve
Michael Stoll
In this paper, we study bounds for the number of rational points on twists C' of a fixed curve C over a number field K, under the condition that the group of K-rational points on t…