Definition 45.5.1 (0FGL)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 45: Weil Cohomology Theories
Section 45.5: Chow groups of motives
Definition 45.5.1 (cite)

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Definition 45.5.1. Let $k$ be a base field. Let $M = (X, p, m)$ be a Chow motive over $k$ . For $i \in \mathbf{Z}$ we define the $i$ th Chow group of $M$ by the formula

$\mathop{\mathrm{CH}}\nolimits ^ i(M) = p\left(\mathop{\mathrm{CH}}\nolimits ^{i + m}(X) \otimes \mathbf{Q}\right)$

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