Picard groups of derived categories

We investigate the group Pic(D.n) of isomorphism classes of invertible objects in the derived category of O-modules for a commutative unital ringed Grothendieck topos (E,O) with enough points. When the ring O-P has connected prime ideal spectrum for all points p of E we show that Pic(D,n) is naturally isomorphic to the Cartesian product of the Picard group of O-modules and the additive group of continuous functions from the space of isomorphism classes of points of E to the integers Z. Also, for a commutative unital ring R, the group Pic(D-R) is isomorphic to the Cartesian product of Pic(R) and the additive group of continuous functions from spec R to the integers Z. (C) 2003 Elsevier Science B.V. All rights reserved.