Barcelona Fall Workshop on Number Theory
Construction of CM genus 3 curves: a survey and first results
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Abstract
Construction of curves with a given number of points over finite fields is useful for cryptography purposes. The main method to construct such curves is the CM method. For genus 3 curves, this method still presents so many gaps. Recently, some improvements has been achieve for some particular families, namely, hyperelliptic curves and Picard curves. We will discuss these last results and new directions of research.
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