The 2-adic valuation of the cardinality of Jacobians of genus 2 curves over quadratic towers of finite fields
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2018Suggested citation
Garra Oronich, Ricard;
Miret, Josep M. (Josep Maria);
Pujolàs Boix, Jordi;
Thériault, Nicolas;
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(2018)
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The 2-adic valuation of the cardinality of Jacobians of genus 2 curves over quadratic towers of finite fields.
Journal of Algebra and Its Applications, 2019, vol. 18, núm. 7, p. 1950135.
https://doi.org/10.1142/S0219498819501354.
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Abstract
Given a genus 2 curve C defined over a finite field Fq of odd characteristic such that 2|#Jac(C)(Fq), we study the growth of the 2-adic valuation of the cardinality of the Jacobian over a tower of quadratic extensions of Fq. In the cases of simpler regularity, we determine the exponents of the 2-Sylow subgroup of Jac(C)(Fq2k).