@techreport{21d5a279c8ce419b841d62e4bf6353f5,

title = "Frobenius lifts and point counting for smooth curves",

abstract = " We describe an algorithm to compute the zeta-function of a proper, smooth curve over a finite field, when the curve is given together with some auxiliary data. Our method is based on computing the matrix of the action of a semi-linear Frobenius on the first cohomology group of the curve by means of Serre duality. The cup product involved can be computed locally, after first computing local expansions of a globally defined lift of Frobenius. The resulting algorithm's complexity is softly cubic in the field degree, which is also the case with Kedlaya's algorithm in the hyperelliptic case. ",

keywords = "math.AG, math.NT, 14F30, 14G10, 14G15, 14Q50 (Primary) 14G22 (Secondary)",

author = "Amnon Besser and Fran{\c c}ois-Renaud Escriva and Jeu, {Rob de}",

note = "29 pages, 2 figures",

year = "2013",

month = jun,

day = "21",

language = "אנגלית",

series = "arXiv preprint arXiv:1903.05382",

type = "WorkingPaper",

}