Rigid cohomology and p-adic point counting
نویسندگان
چکیده
منابع مشابه
Rigid cohomology and p - adic point counting ∗
I consider the problem of computing the zeta function of an algebraic variety defined over a finite field. This problem has been pushed into the limelight in recent years because of its importance in cryptography, at least in the case of curves. Wan’s excellent survey article gives an overview of what has been achieved, and what remains to be done, on the topic [15]. The purpose of this exposit...
متن کاملRigid cohomology and p - adic point counting par
I discuss some algorithms for computing the zeta function of an algebraic variety over a finite field which are based upon rigid cohomology. Two distinct approaches are illustrated with a worked example.
متن کاملRigid cohomology and p - adic point counting par ALAN
I discuss some algorithms for computing the zeta function of an algebraic variety over a finite field which are based upon rigid cohomology. Two distinct approaches are illustrated with a worked example.
متن کاملQuasi-quadratic elliptic curve point counting using rigid cohomology
We present a deterministic algorithm that computes the zeta function of a nonsupersingular elliptic curve E over a finite field with p elements in time quasi-quadratic in n. An older algorithm having the same time complexity uses the canonical lift of E, whereas our algorithm uses rigid cohomology combined with a deformation approach. An implementation in small odd characteristic turns out to g...
متن کاملp-adic Cohomology
The purpose of this paper is to survey some recent results in the theory of “p-adic cohomology”, by which we will mean several different (but related) things: the de Rham or p-adic étale cohomology of varieties over p-adic fields, or the rigid cohomology of varieties over fields of characteristic p > 0. Our goal is to update Illusie’s beautiful 1994 survey [I] by reporting on some of the many i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2005
ISSN: 1246-7405
DOI: 10.5802/jtnb.484