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What is generally known as the “Bloch–Srinivas method” consists of decomposing the diagonal of a smooth projective variety, and then considering the action of correspondences in cohomology. In this note, we observe that this same method can also be extended to singular and quasi-projective varieties. We give two applications of this observation: the first is a version of Mumford’s theorem, the second...
A theorem of Jannsen asserts that if a smooth projective variety has injective cycle class maps, it has surjective cycle class maps. The object of this note is to present a version of Jannsen’s theorem for singular quasi-projective varieties.
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