Multiple supersingular elliptic fibers on elliptic surfaces
نویسندگان
چکیده
منابع مشابه
Constructing Supersingular Elliptic Curves
We give an algorithm that constructs, on input of a prime power q and an integer t, a supersingular elliptic curve over Fq with trace of Frobenius t in case such a curve exists. If GRH holds true, the expected run time of our algorithm is e O((log q)). We illustrate the algorithm by showing how to construct supersingular curves of prime order. Such curves can readily be used for pairing based c...
متن کاملLocal GW Invariants of Elliptic Multiple Fibers
We use simple geometric arguments to calculate the dimension zero local Gromov-Witten invariants of elliptic multiple fibers. This completes the calculation of all dimension zero GW invariants of elliptic surfaces with pg > 0. Let X be a Kähler surface with pg > 0. By the Enriques-Kodaira classification (cf. [BHPV]), its minimal model is a K3 or Abelian surface, a surface of general type or an ...
متن کاملOn Elliptic K3 Surfaces
We make a complete list of all possible ADE-types of singular fibers of complex elliptic K3 surfaces and the torsion parts of their MordellWeil groups.
متن کاملMinimal Cm Liftings of Supersingular Elliptic Curves
In this paper, we give a ‘direct’ construction of the endomorphism ring of supersingular elliptic curves over a prime field Fp from ‘ideal classes’ of Q( √−p). We use the result to prove that the result of Kaneko on ‘minimal’ CM liftings of such supersingular elliptic curves is a best possible result. We also prove that the result of Elkies on ‘minimal’ CM liftings of all supersingular elliptic...
متن کاملCM liftings of supersingular elliptic curves
Assuming GRH, we present an algorithm which inputs a prime p and outputs the set of fundamental discriminants D < 0 such that the reduction map modulo a prime above p from elliptic curves with CM by OD to supersingular elliptic curves in characteristic p. In the algorithm we first determine an explicit constant Dp so that |D| > Dp implies that the map is necessarily surjective and then we compu...
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 of Pure and Applied Algebra
سال: 2006
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2005.06.009