Picard groups of derived categories

We investigate the group of isomorphism classes of invertible objects in the derived category of -modules for a commutative unital ringed Grothendieck topos with enough points. When the ring has connected prime ideal spectrum for all points p of we show that is naturally isomorphic to the Cartesian product of the Picard group of -modules and the additive group of continuous functions from the space of isomorphism classes of points of to the integers . Also, for a commutative unital ring R, the group is isomorphic to the Cartesian product of Pic(R) and the additive group of continuous functions from spec R to the integers .