The Web of Data has been gaining momentum and this leads to increasingly publish more semi-structured datasets following the RDF model, based on atomic triple units of subject, predicate, and object. Although it is a simple model, compression methods become necessary because datasets are increasingly larger and various scalability issues arise around their organization and storage. This requirement is more restrictive in RDF stores because efficient SPARQL resolution on the compressed RDF datasets is also required. This article introduces a novel RDF indexing technique (called k2-triples) supporting efficient SPARQL resolution in compressed space. k2-triples, uses the predicate to vertically partition the dataset into disjoint subsets of pairs (subject, object), one per predicate. These subsets are represented as binary matrices in which 1-bits mean that the corresponding triple exists in the dataset. This model results in very sparse matrices, which are efficiently compressed using k2-trees. We enhance this model with two compact indexes listing the predicates related to each different subject and object, in order to address the specific weaknesses of vertically partitioned representations. The resulting technique not only achieves by far the most compressed representations, but also the best overall performance for RDF retrieval in our experiments. Our approach uses up to 10 times less space than a state of the art baseline, and outperforms its performance by several order of magnitude on the most basic query patterns. In addition, we optimize traditional join algorithms on k2-triples and define a novel one leveraging its specific features. Our experimental results show that our technique overcomes traditional vertical partitioning for join resolution, reporting the best numbers for joins in which the non-joined nodes are provided, and being competitive in the majority of the cases.