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

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Abstract

Given a smooth projective variety X">X over a field, consider the Q">Q-vector space Z0(X)">Z0(X) of 0-cycles (that is, formal finite Q">Q-linear combinations of closed points of X">X) as a module over the algebra of finite correspondences. Then the rationally trivial 0-cycles on X">X form an absolutely simple and essential submodule of Z0(X)">Z0(X).

About the authors

Marat Zefirovich Rovinskii

Laboratory of algebraic geometry and its applications, National Research University "Higher School of Economics" (HSE); Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)

Author for correspondence.
Email: marat@mccme.ru
Doctor of physico-mathematical sciences

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