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Generalizing Kedlaya's order counting based on Miura Theory
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Abstract: | 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 G\"{u}rel) 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. |
BibTeX
@misc{eprint-2004-12101, title={Generalizing Kedlaya's order counting based on Miura Theory}, booktitle={IACR Eprint archive}, keywords={foundations / Kedlaya, Miura, order counting, elliptic curves}, url={http://eprint.iacr.org/2004/129}, note={ suzuki@math.sci.osaka-u.ac.jp 12568 received 30 May 2004}, author={Joe Suzuki}, year=2004 }