Ivan Pogildiakov - Academia.edu (original) (raw)
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Papers by Ivan Pogildiakov
arXiv: Algebraic Geometry, 2017
An irreducible smooth projective curve over mathbbFq\mathbb{F}_qmathbbFq is called \textit{pointless} if it has... more An irreducible smooth projective curve over mathbbFq\mathbb{F}_qmathbbFq is called \textit{pointless} if it has no mathbbFq\mathbb{F}_qmathbbFq-rational points. In this paper we study the lower existence bound on the genus of such a curve over a fixed finite field mathbbFq\mathbb{F}_qmathbbFq. Using some explicit constructions of hyperelliptic curves, we establish two new bounds that depend linearly on the number qqq. In the case of odd characteristic this improves upon a result of R. Becker and D. Glass. We also provide a similar new bound when qqq is even.
arXiv: Algebraic Geometry, 2017
An irreducible smooth projective curve over mathbbFq\mathbb{F}_qmathbbFq is called \textit{pointless} if it has... more An irreducible smooth projective curve over mathbbFq\mathbb{F}_qmathbbFq is called \textit{pointless} if it has no mathbbFq\mathbb{F}_qmathbbFq-rational points. In this paper we study the lower existence bound on the genus of such a curve over a fixed finite field mathbbFq\mathbb{F}_qmathbbFq. Using some explicit constructions of hyperelliptic curves, we establish two new bounds that depend linearly on the number qqq. In the case of odd characteristic this improves upon a result of R. Becker and D. Glass. We also provide a similar new bound when qqq is even.