Pontryagin products and adequate equivalence relations
نویسنده
چکیده
Let A be an abelian variety over an algebraically closed field. The Chow group CH0(A) of zero-dimensional cycles modulo rational equivalence forms a ring under the Pontryagin product operation with respect to which the subset I of degree zero cycles is an ideal. The nth power of I is shown to agree with the nth power of the algebraic equivalence relation as defined by H. Saito. A result is also proven relating products of equivalence relations (in the relative setting) to the decomposition of the Chow motive of an abelian variety.
منابع مشابه
Adequate equivalence relations and Pontryagin products
Let A be an abelian variety over a field k. We consider CH0(A) as a ring under Pontryagin product and relate powers of the ideal I ⊆ CH0(A) of degree zero elements to powers of the algebraic equivalence relation. We also consider a filtration F 0 ⊇ F 1 ⊇ . . . on the Chow groups of varieties of the form T ×k A (defined using Pontryagin products on A ×k A considered as an A-scheme via projection...
متن کاملFUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS
In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...
متن کاملBordism and the Pontryagin-Thom Theorem
Given the classification of low dimensional manifolds up to equivalence relations such as diffeomorphism or homeomorphism, one would hope to be able to continue to classify higher dimensional manifolds. Unfortunately, this turns out to be difficult or impossible, and so one solution would be turn to some weaker equivalence relation. One such equivalence relation would be to consider manifolds u...
متن کاملOn certain semigroups of transformations that preserve double direction equivalence
Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E}It is known that TE(X) is a subsemigroup of TX. In this paper, we discussthe Green's *-relations, certain *-ideal and certain Rees quotient semigroup for TE(X).
متن کاملQuantum E(2) group and its Pontryagin dual
The quantum deformation of the group of motions of the plane and its Pontryagin dual are described in details. It is shown that the Pontryagin dual is a quantum deformation of the group of transformations of the plane generated by translations and dilations. An explicite expression for the unitary bicharacter describing the Pontryagin duality is found. The Heisenberg commutation relations are w...
متن کامل