Jazz is global, but its most ambitious players still flock to the US to soak in its roots and prove they’re part of the scene. Tonight a Parisian septet called Fractale wraps up an eight-gig tour of the States at the Drom in the East Village, after stops in New Orleans, Cleveland and Chicago. From December 3 to 6 Spanish pianist Chano DomÃnguez & his Flamenco Quintet bring its commissioned “The Flamenco Side of Kind of Blue” to the Jazz Standard to assert that the Barcelona Jazz Festival (in which they premiere the work on November 12) has something to do with the Big Apple. Next February the Portland Jazz Festival explores the theme “Is Jazz Dead (Or Has It Moved To A New Address?).” But incontrovertible evidence suggests that however far the sound has spread, those who matter know where jazz calls home.