We make explicit Serre's generalization of the Sato-Tate conjecture formotives, by expressing the construction in terms of fiber functors from themotivic category of absolute Hodge cycles into a suitable category of Hodgestructures of odd weight. This extends the case of abelian varietes, which wetreated in a previous paper. That description was used byFite--Kedlaya--Rotger--Sutherland to classify Sato-Tate groups of abeliansurfaces; the present description is used by Fite--Kedlaya--Sutherland to makea similar classification for certain motives of weight 3. We also giveconditions under which verification of the Sato-Tate conjecture reduces to theidentity connected component of the corresponding Sato-Tate group.
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