A finiteness theorem for algebraic cycles

2010/03/25 by Peter O’Sullivan, O'Sullivan, Peter
Computer Science · Mathematics · Physics and Astronomy · #14C15 #14C25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1003.4789

openalex publication_date 2010/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective variety. Starting with a finite set of cycles on powers X^m of X, we consider the Q-vector subspaces of the Q-linear Chow groups of the X^m obtained by iterating the algebraic operations and pullback and push forward along those morphisms X^l -> X^m for which each component X^l -> X is a projection. It is shown that these Q-vector subspaces are all finite-dimensional, provided that the Q-linear Chow motive of X is a direct summand of that of an abelian variety.

Citations

• Nilpotence, radicaux et structures mono"ıdales

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