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Computing the 2-adic Canonical Lift of Genus 2 Curves

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Abstract

Let k be a field of even characteristic and M2(k) the moduli space of the genus 2 curves defined over k. We first compute modular polynomials in function of invariants with good reduction modulo two. We then use these modular polynomials to compute the canonical lift of genus 2 curves in even characteristic. The lifted Frobenius is characterized by the reduction behaviors of the Weierstrass points over k. This allows us to compute the cardinality of the Jacobian variety. We give a detailed description with the necessary optimizations for an efficient implementation.
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Dates and versions

hal-03119147 , version 1 (22-01-2021)

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  • HAL Id : hal-03119147 , version 1

Cite

Abdoulaye Maiga, Damien Robert. Computing the 2-adic Canonical Lift of Genus 2 Curves. ICMC 2021 - 7th International Conference on Mathematics and Computing, Indian Institute of Engineering Science and Technology, Mar 2021, Shibpur / Virtual, India. ⟨hal-03119147⟩
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