Understanding the causal genetic architecture of complex phenotypes will fuel future research into disease mechanisms and potential therapies. Here, we illustrate the power of a novel framework: it detects, starting from summary statistics, and across the entire genome, sets of variants that carry non-redundant information on the phenotypes and are therefore more likely to be causal in a biological sense. The approach, implemented in open-source software, is also computationally efficient, requiring less than 15 minutes on a single CPU to perform genome-wide analysis. Through extensive genome-wide simulation studies, we show that the method can substantially outperform existing methods in false discovery rate control, statistical power and various fine-mapping criteria. In applications to a meta-analysis of ten large-scale genetic studies of Alzheimer's disease (AD), we identified 82 loci associated with AD, including 37 additional loci missed by conventional GWAS pipeline. Massively parallel reporter assays and CRISPR-Cas9 experiments have confirmed the functionality of the putative causal variants our method points to. Finally, we retrospectively analyzed summary statistics from 67 large-scale GWAS for a variety of phenotypes. Results reveal the method's capacity to robustly discover additional loci for polygenic traits and pinpoint potential causal variants underpinning each locus beyond conventional GWAS pipeline, contributing to a deeper understanding of complex genetic architectures in post-GWAS analyses.