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arXiv · 2310.11218

Closed points on curves over finite fields

Yves Aubry·Fabien Herbaut·Julien Monaldi
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Abstract

We are interested in the quantity $\rho$(q, g) defined as the smallest positive integer such that r $\ge$ $\rho$(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.

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Yves Aubry, Fabien Herbaut, Julien Monaldi. 2023-10-17. Closed points on curves over finite fields. https://arxiv.org/abs/2310.11218

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