The existence of supersingular curves of genus 4 in arbitrary characteristic
نویسندگان
چکیده
منابع مشابه
On the Existence of Supersingular Curves Of Given Genus
In this note we shall show that there exist supersingular curves for every positive genus in characteristic 2. Recall that an irreducible smooth algebraic curve C over an algebraically closed field F of characteristic p > 0 is called supersingular if its jacobian is isogenous to a product of supersingular elliptic curves. An elliptic curve is called supersingular if it does not have points of o...
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Let C be a supersingular genus-2 curve over an algebraically closed field of characteristic 3. We show that if C is not isomorphic to the curve y = x + 1 then up to isomorphism there are exactly 20 degree-3 maps φ from C to the elliptic curve E with j-invariant 0. We study the coarse moduli space of triples (C, E, φ), paying particular attention to questions of rationality. The results we obtai...
متن کاملSome Families of Supersingular Artin-schreier Curves in Characteristic > 2
A curve over finite field is supersingular if its Jacobian is supersingular as an abelian variety. On the one hand, supersingular abelian varieties form the smallest (closed) stratum in the moduli space of abelian varieties, on the other the intersection of Jacobian locus and the stratification of moduli space is little known. Consequently it is very difficult to locate a family of supersingula...
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We consider digital expansions of scalars for supersingular Koblitz curves in characteristic three. These are positional representations of integers to the base of τ , where τ is a zero of the characteristic polynomial T 2 ± 3T + 3 of a Frobenius endomorphism. They are then applied to the improvement of scalar multiplication on the Koblitz curves. A simple connection between τ -adic expansions ...
متن کاملPairing Calculation on Supersingular Genus 2 Curves
In this paper we describe how to efficiently implement pairing calculation on supersingular genus 2 curves over prime fields. We find that, contrary to the results reported in [8], pairing calculation on supersingular genus 2 curves over prime fields is efficient and a viable candidate for practical implementation. We also show how to eliminate divisions in an efficient manner when computing th...
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ژورنال
عنوان ژورنال: Research in Number Theory
سال: 2020
ISSN: 2522-0160,2363-9555
DOI: 10.1007/s40993-020-00217-x