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We discuss the geometry of the Ramond-Ramond fields of low degree via thelanguage of abelian p-gerbes, working in type II superstring theory withvanishing H-flux. A Dp-brane is a source for the Ramond-Ramond field strengthG_(p+2), which can be thought of as the curvature of a connection on a p-gerbewith U(1)-band. The highest degree forms of the connection are the localRamond-Ramond potentials C_(p+1). This picture is clear for p >= 0, a 0-gerbebeing a line bundle. Actually, one can encounter also lower degreeRamond-Ramond field strengths: G_1 in IIB superstring theory, and G_0 in IIAsuperstring theory. Although the geometrical nature of these objects is simplein itself, it is interesting to explicitly clarify the analogy with thegeometry of the higher degree fields and potentials, introducing the notions of(-1)-gerbes with connection and (-2)-gerbes. We define these gerbes and we showthat they are better described by a variant of ordinary Cech cohomology.

Topics on the geometry of D-brane charges and Ramond-Ramond fields - Part II: Low-degree RR fields