Computing the p-Selmer Group of an Elliptic Curve
... algorithm for computing Selmer groups of Jacobians. The algorithm relies on two assumptions. The rst requires there to be a rational divisor class of degree relatively prime to the exponent of the kernel of the isogeny. This is guaranteed in our case by the fact that an elliptic curve has a rationa ...
... algorithm for computing Selmer groups of Jacobians. The algorithm relies on two assumptions. The rst requires there to be a rational divisor class of degree relatively prime to the exponent of the kernel of the isogeny. This is guaranteed in our case by the fact that an elliptic curve has a rationa ...
General Topology II - National Open University of Nigeria
... W. Thus the collection D meets the criterion of proposition 3.2. so D is a basis of X × Y. Example 3.13 You have the standard topology of R. The product topology of this topology with itself is called the Product topology on R × R = R2 . It has as basis the collection of all products of open sets of ...
... W. Thus the collection D meets the criterion of proposition 3.2. so D is a basis of X × Y. Example 3.13 You have the standard topology of R. The product topology of this topology with itself is called the Product topology on R × R = R2 . It has as basis the collection of all products of open sets of ...
- Journal of Linear and Topological Algebra
... multifunctions was first codified by Berge [10]. In the last three decades, the theory of multifunctions has advanced in a variety of ways and applications of this theory, can be found for example, in economic theory, noncooparative games, artificial intelligence, medicine, information sciences and ...
... multifunctions was first codified by Berge [10]. In the last three decades, the theory of multifunctions has advanced in a variety of ways and applications of this theory, can be found for example, in economic theory, noncooparative games, artificial intelligence, medicine, information sciences and ...
(pdf)
... t ◦ s = u = 1W . Interchanging the roles of W and X × Y in this argument, we conclude also that s ◦ t = 1X×Y . This proves that the homomorphism s : W → X × Y has an inverse t : X × Y → W , and hence s is a unique isomorphism from W to X × Y commuting with the projections. This observation that the ...
... t ◦ s = u = 1W . Interchanging the roles of W and X × Y in this argument, we conclude also that s ◦ t = 1X×Y . This proves that the homomorphism s : W → X × Y has an inverse t : X × Y → W , and hence s is a unique isomorphism from W to X × Y commuting with the projections. This observation that the ...
FIBRATIONS OF TOPOLOGICAL STACKS Contents 1. Introduction 2
... We do not know if Proposition 2.7 remains true when the maps i or j are not embeddings, or when X is an arbitrary topological stack. It appears though that, even when (Y, A) is a nice pair (say an inclusion of a finite CW complex into another), the quotient space Y /A may not in general have the uni ...
... We do not know if Proposition 2.7 remains true when the maps i or j are not embeddings, or when X is an arbitrary topological stack. It appears though that, even when (Y, A) is a nice pair (say an inclusion of a finite CW complex into another), the quotient space Y /A may not in general have the uni ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.