搜索结果: 1-15 共查到“数论 Curves”相关记录16条 . 查询时间(0.14 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Vanishing of some algebraic cycles on powers of Shimura curves
志村曲线 幂 代数 循环消失
2023/4/27
For a smooth projective variety over a number field, the Beilinson—Bloch conjecture predicts that Chow groups of algebraic cycles modulo rational equivalence can be determined using cohomological data...
商洛学院数学与计算机应用学院初等数论课件Chapter 6 Elliptic Curves
商洛学院数学与计算机应用学院 初等数论 课件 Chapter 6 Elliptic Curves
2017/4/7
商洛学院数学与计算机应用学院初等数论课件Chapter 6 Elliptic Curves.
A Cohen-Lenstra phenomenon for elliptic curves
A Cohen-Lenstra phenomenon elliptic curves Number Theory
2012/6/29
Given an elliptic curve $E$ and a finite Abelian group $G$, we consider the problem of counting the number of primes $p$ for which the group of points modulo $p$ is isomorphic to $G$. Under a certain ...
Heegner points and Jochnowitz congruences on Shimura curves
Heegner points Shimura curves L-functions Jochnowitz congruences
2012/4/18
Given a rational elliptic curve E, a suitable imaginary quadratic field K and a quaternionic Hecke eigenform g of weight 2 obtained from E by level raising such that the sign in the functional equatio...
On Zagier's conjecture for base extensions of elliptic curves
Zagier's conjecture base extensions of elliptic curves Number Theory
2012/4/18
Let E be an elliptic curve over Q, and let F be a finite abelian extension of Q. Using Beilinson's theorem on a suitable modular curve, we prove a weak version of Zagier's conjecture for L(E/F,2), whe...
On the Surjectivity of Galois Representations Associated to Elliptic Curves over Number Fields
Surjectivity Galois Representations Elliptic Curves over Number Fields Number Theory
2012/4/17
Given an elliptic curve $E$ over a number field $K$, the $\ell$-torsion points $E[\ell]$ of $E$ define a Galois representation $\gal(\bar{K}/K) \to \gl_2(\ff_\ell)$. A famous theorem of Serre states t...
Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
Pairing-based algorithms jacobians of genus 2 curves maximal endomorphism ring Number Theory
2012/4/17
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the $\ell$-Tate pairing in terms of the action of the Frobenius on the $\ell$-torsion of the Jacobian of a ge...
Non-existence of elliptic curves with everywhere good reduction over some real quadratic fields
Non-existence of elliptic curves quadratic fields Number Theory
2011/9/19
Abstract: We prove the non-existence of elliptic curves having good reduction everywhere over some real quadratic fields.
Cubic Curves, Finite Geometry and Cryptography
Cubic curves group law non-singularity elliptic curve cryptography finite geometries
2011/9/19
Abstract: Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group st...
Explicit n-descent on elliptic curves. III. Algorithms
Explicit n-descent elliptic curves Algorithms Number Theory
2011/9/14
Abstract: This is the third in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as genus one normal curves of degree n. The metho...
Identifying supersingular elliptic curves
Identifying supersingular elliptic curves Number Theory
2011/8/26
Abstract: Given an elliptic curve E over a field of characteristic p, we consider how to efficiently determine whether E is ordinary or supersingular. We analyze the complexity of several existing alg...
Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence
Shimura curves p-adic Jacquet-Langlands correspondence Number Theory
2011/8/25
Abstract: We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. ...
A mean value formula for elliptic curves
elliptic curves Weierstrass ℘ -function point multiplication division polynomial
2011/8/24
Abstract: It is proved in this paper that for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate and that of y-coordinates of its ...
Heuristics on pairing-friendly elliptic curves
Elliptic curves finite fields pairing-based cryptography
2011/8/23
Abstract: We present a heuristic asymptotic formula as $x\to \infty$ for the number of pairing-friendly elliptic curves with fixed embedding degree $k\geq 3$, with fixed discriminant, with rho-value b...
Gromov-Witten invariants and rational curves on Grassmannians
Gromov-Witten invariants rational curves on Grassmannians
2010/11/15
We study the enumerative significance of the s-pointed genus zero Gromov-Witten invariant on a homogeneous space X. For that, we give an interpretation in terms of rational curves on X.