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Computing the 2-adic Canonical Lift of Genus 2 Curves

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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https://hal.inria.fr/hal-03119147
Contributor : Damien Robert Connect in order to contact the contributor
Submitted on : Friday, January 22, 2021 - 9:59:52 PM
Last modification on : Saturday, December 4, 2021 - 3:44:00 AM
Long-term archiving on: : Friday, April 23, 2021 - 7:39:47 PM

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

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