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The 2-adic valuation of the cardinality of Jacobians of genus 2 curves over quadratic towers of finite fields

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Issue date
2018
Author
Garra Oronich, Ricard
Miret, Josep M. (Josep Maria)
Pujolàs Boix, Jordi
Thériault, Nicolas
Suggested citation
Garra Oronich, Ricard; Miret, Josep M. (Josep Maria); Pujolàs Boix, Jordi; Thériault, Nicolas; . (2018) . 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).
URI
http://hdl.handle.net/10459.1/65082
DOI
https://doi.org/10.1142/S0219498819501354
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Journal of Algebra and Its Applications, 2019, vol. 18, núm. 7, p. 1950135
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