Bruno was denounced to the Venetian Inquisition by his own patron Giovanni Mocenigo in May 1592, transferred to Rome, held for seven years, refused to recant in December 1599, and was burned at the Campo de' Fiori on 17 February 1600.
The nineteenth century made him the martyr of science, executed for teaching that the earth moves. That is not sustainable. Copernicus's De revolutionibus was not placed on the Index until 1616, sixteen years after Bruno died; heliocentrism was not a heresy in 1600 and he cannot have been condemned for holding it.
The charge list, reconstructed by Luigi Firpo from the Sommario of the trial that Angelo Mercati found in the Vatican archives in 1940, is theological almost throughout: denial of the Trinity, of the divinity of Christ, of the Incarnation, of the virginity of Mary and of transubstantiation, together with metempsychosis, the practice of magic and divination, and the plurality and eternity of worlds. The document containing the eight propositions finally put to him is lost, so the exact final formulation cannot be checked.
The defensible statement is therefore narrower than either legend. He was condemned as a theological heretic, and he was one, he denied central Christian doctrines and said so repeatedly. His cosmology entered the case, but as metaphysics and theology rather than as astronomy: an infinity of worlds and an eternal universe bear on creation, providence and the uniqueness of the Incarnation, which is why they are on the list. Not a martyr for Copernicanism; not unconnected to his cosmology either.