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

M. Z. Rovinsky<sup>ab

a</sup> Laboratory of Algebraic Geometry and Its Applications, National Research University Higher School of Economics, Moscow, Russia
^b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia

Abstract: 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.

Keywords: 0-cycles, filtrations on 0-cycles, finite correspondences.

MSC: 14C15, 14C25

Received: 13.03.2023 and 26.03.2023

DOI: 10.4213/sm9907

 English version: Sbornik: Mathematics, 2023, 214:8, 1153–1162

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