3 papers
math.AG2026
Computing Picard Schemes
Hyuk Jun Kweon, Madhavan Venkatesh
We present an algorithm to compute the torsion component of the Picard scheme of a smooth projective variety over a field . Specifically, we describe $\mat…
math.NT2025
Counting points on surfaces in polynomial time
Nitin Saxena, Madhavan Venkatesh
We present a randomised algorithm to compute the local zeta function of a fixed smooth, projective surface over , at any large prime of good reduction. The runtime…
cs.CC2025
Complexity of counting points on curves and the factor of the zeta function of surfaces
Diptajit Roy, Nitin Saxena, Madhavan Venkatesh
This article concerns the computational complexity of a fundamental problem in number theory: counting points on curves and surfaces over finite fields. There is no subexponential-…