Extending locally truncated chamber Systems by sheaves

Abstract

Abstract. We generalize the theory of sheaves to chamber systems. We prove that, given a chamber system ^ and a family ^ of proper residues of # containing all residues of rank <1, every sheaf defined over & admits a completion which extends #. We also prove that, under suitable hypotheses, a sheaf defined over a truncation of # can be extended to a sheaf for #. In the last section of this paper, we apply these results to a number of special cases.