semistable，DeRham，Hogde-Tate，其中前面能够推出后面，Tate的猜想相当于说是X的etale上同调是Hodge-Tat...
泰特提出了大量重要的数学思想,许多概念都以他的名字命名,比如泰特代数(Tate algebra)、泰特定理(Tate theorem)、泰特猜想(Tate conjecture)、泰特对偶性(Tate duality)、泰特模(Tate module)、泰特群(Tate group)、泰特曲线(Tate curve)、泰特上同调(Tate coho...
Hilbert Class Polynomials of imaginary quadratic orders play an important role here. We give a global application to the study of prime-splitting in torsion fields of elliptic curves over number fields. 展开 关键词: Elliptic curve integral Tate module reciprocity law DOI: 10.1142/S1793042116500147...
integral Tate modulereciprocity lawLet E be an elliptic curve over a finite field k, and u2113 a prime number different from the characteristic of k. In this paper, we consider the problem of finding the structure of the Tate module Tu2113(E) as an integral Galois representations of k. ...
This paper shows our experimental results of Cheon’s algorithm by implementing it with some speeding-up techniques. In fact, we succeeded to solve DLPwAI in a group with 128-bit order in 45 hours with a single PC on an elliptic curve defined over a prime finite field with 256-bit ...
As a testimony to Tate’s stature in the fields ofnumber theoryandalgebraic geometry, many concepts used in thosedisciplinesbear his name—e.g., the Tate twist, the Tate-Shafarevich group, the Tate module, Tate cohomology, the Tate duality theorem, the Tate trace, Hodge-Tate decompositions, ...
和abelian variety算数性质的研究也是奠基性的 比如Serre-Tate对good reduction的理解, Tate module的发现...
11. The method as recited in claim 2, wherein determining said pairings for use in cryptographically processing said selected information further includes: determining at least a first function and a second function that are associated to certain multiples of a point on said elliptic curve; determin...
The paper deals with the group of locally trivial principal homogeneous spaces over an elliptic curve. Duality is proven between the group of those spaces having a point of finite order locally with the exception of prime divisors, and the factor group of those of them which are infinitely ...
The set of K-rational points on an elliptic curve, E, are known to form a finitely generated abelian group. My results are of interest when trying to find the rank of this group, which in general is a hard problem. The Selmer group of E,S(E/K), can be used to give a bound on...