The 2-adic valuation of the cardinality of Jacobians of genus 2 curves over quadratic towers of finite fields
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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).
Is part ofJournal of Algebra and Its Applications, 2019, vol. 18, núm. 7, p. 1950135
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