You are looking at a specific version 20040603:190134 of this paper. See the latest version.

Paper 2004/129

Generalizing Kedlaya's order counting based on Miura Theory

Joe Suzuki

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 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.

Metadata
Available format(s)
PDF PS
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
KedlayaMiuraorder countingelliptic curves
Contact author(s)
suzuki @ math sci osaka-u ac jp
History
2004-06-03: received
Short URL
https://ia.cr/2004/129
License
Creative Commons Attribution
CC BY
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.