Closed points on curves over finite fields
Algebraic Geometry
2023-10-18 v1
Abstract
We are interested in the quantity (q, g) defined as the smallest positive integer such that r (q, g) implies that any absolutely irreducible smooth projective algebraic curve defined over F q of genus g has a closed point of degree r. We provide general upper bounds for this number and its exact value for g = 1, 2 and 3. We also improve the known upper bounds on the number of closed points of degree 2 on a curve.
Cite
@article{arxiv.2310.11218,
title = {Closed points on curves over finite fields},
author = {Yves Aubry and Fabien Herbaut and Julien Monaldi},
journal= {arXiv preprint arXiv:2310.11218},
year = {2023}
}