5 citations · 5 across the 1 of their papers we have counts for
5 papers
Quadratic Chabauty for modular curves: Algorithms and examples
Jennifer S. Balakrishnan, Netan Dogra, Jan Steffen Müller +2
We describe how the quadratic Chabauty method may be applied to explicitly determine the set of rational points on modular curves of genus whose Jacobians have Mordell--Weil…
Explicit Chabauty-Kim for the Split Cartan Modular Curve of Level 13
Jennifer S. Balakrishnan, Netan Dogra, J. Steffen Müller +2
We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in an algorithm to compu…
Explicit Coleman integration for curves
Jennifer S. Balakrishnan, Jan Tuitman
The Coleman integral is a -adic line integral that plays a key role in computing several important invariants in arithmetic geometry. We give an algorithm for explicit Coleman i…
Computing zeta functions of generic projective hypersurfaces in larger characteristic
Jan Tuitman
We give improvements of the deformation method for computing the zeta function of a generic projective hypersurface in characteristic~ that either reduce the dependence on~ o…
Point counting on curves using a gonality preserving lift
Wouter Castryck, Jan Tuitman
We study the problem of lifting curves from finite fields to number fields in a genus and gonality preserving way. More precisely, we sketch how this can be done efficiently for cu…