A remark on 0-cycles as modules over algebras of finite correspondences

doi:10.4213/sm9907e

Marat Zefirovich Rovinskii

A remark on 0-cycles as modules over algebras of finite correspondences

Algebra and Number Theory

Given a smooth projective variety $X$ over a field, consider the $\mathbb Q$-vector space $Z_0(X)$ of 0-cycles (that is, formal finite $\mathbb Q$-linear combinations of closed points of $X$) as a module over the algebra of finite correspondences. Then the rationally trivial 0-cycles on $X$ form an absolutely simple and essential submodule of $Z_0(X)$. Bibliography: 15 titles.

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