This question is a continuation of Varieties with Chow groups supported in positive codimension: examples and properties?

What examples are known of morphisms of varieties and Chow motives (say, over complex numbers) such that the pushforward map on $Chow_0$ (the group of $0$-cycles modulo rational equivalence) is an epimorphism or an isomorphism, and possibly the same is true for on $Chow_1$? I would like to have an example that is rather "compicated", so that (1) one cannot compute the groups in question themselves and (2) the isomorphism in question cannot be established using a "simple" general (motivic or intersection theory) argument.

This question is a continuation of Varieties with Chow groups supported in positive codimension: examples and properties?

What examples are known of morphisms of varieties and Chow motives (say, over complex numbers) such that the pushforward map on $Chow_0$ (the group of $0$-cycles modulo rational equivalence) is an epimorphism or an isomorphism, and possibly the same is true for on $Chow_1$? I would like to have an example that is rather "compicated", so that (1) one cannot compute the groups in question themselves and (2) the isomorphism in question cannot be established using a "simple" general (motivic or intersection theory) argument.

This question is a contination of Varieties with Chow groups supported in positive codimension: examples and properties?

What examples are known of morphisms of varieties and Chow motives (say, over complex numbers) such that the pushforward map on $Chow_0$ (the group of $0$-cycles modulo rational equivalence) is an epimorphism or isomorphism, and possibly the same is true for on $Chow_1$, and/or also for some 'higher Chow groups of low dimension'? Currently I am only aware of papers that treat embeddings of varieties (composed with birational morphisms).

This question is a continuation of Varieties with Chow groups supported in positive codimension: examples and properties?

What examples are known of morphisms of varieties and Chow motives (say, over complex numbers) such that the pushforward map on $Chow_0$ (the group of $0$-cycles modulo rational equivalence) is an epimorphism or an isomorphism, and possibly the same is true for on $Chow_1$? I would like to have an example that is rather "compicated", so that (1) one cannot compute the groups in question themselves and (2) the isomorphism in question cannot be established using a "simple" general (motivic or intersection theory) argument.

This question is a contination of Varieties with Chow groups supported in positive codimension: examples and properties?

What examples are known of morphisms of varieties and Chow motives (say, over complex numbers) that induce epimorphisms or isomorphisms of theie $Chow_0$-groups ($0$-cycles modulo rational equivalence), and possibly also on $Chow_1$, and/or also on some 'higher Chow groups of low dimension'? Currently I am only aware of papers that treat embeddings of varieties.

This question is a contination of Varieties with Chow groups supported in positive codimension: examples and properties?

What examples are known of morphisms of varieties and Chow motives (say, over complex numbers) such that the pushforward map on $Chow_0$ (the group of $0$-cycles modulo rational equivalence) is an epimorphism or isomorphism, and possibly the same is true for on $Chow_1$, and/or also for some 'higher Chow groups of low dimension'? Currently I am only aware of papers that treat embeddings of varieties (composed with birational morphisms).