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I have recently been learning about pure motives and i have begun to learn about mixed motives, in this paper, motives are written as a triple $h(X,e,n)$ where $e$ is an idempotent endomorphism and $n$ is the tate twist, however, in this paper they seem to be written as $h(X)(n)[m]$, is know that the $(n)$ is a tate twist but what is the $[m]$?

Thanks in advance.

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  • $\begingroup$ The second paper is about the derived category of mixed motives (the abelian category of mixed motives is still conjectural so this is simply a triangulated category which looks like the derived category of mixed motives). The $[m]$ denotes the usual shift in a triangulated category. $\endgroup$
    – Roland
    Apr 1 at 7:08

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