[Resource Topic] 2004/129: Generalizing Kedlaya's order counting based on Miura Theory

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Generalizing Kedlaya’s order counting based on Miura Theory

Authors: Joe Suzuki


K. Kedlaya proposed an method to count the number of {\mathbb F}_q-rational points in a hyper-elliptic curve, using the Leschetz fixed points formula in Monsky-Washinitzer Cohomology. The method has been extended to super-elliptic curves (Gaudry and Gürel) immediately, to characteristic two hyper-elliptic curves, and to C_{ab} curves (J. Denef, F. Vercauteren). Based on Miura theory, which is associated with how a curve is expressed as an affine variety, this paper applies Kedlaya’s method to so-called strongly telescopic curves which are no longer plane curves and contain super-elliptic curves as special cases.

ePrint: https://eprint.iacr.org/2004/129

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