The "omnigenic" hypothesis postulates that the polygenic effects of common SNPs on a typical complex trait are mediated through trans-effects on expression of a relatively sparse set of effector ("core") genes. We tested this hypothesis in a study of 4,964 cases of type 1 diabetes (T1D) and 7,497 controls by using summary statistics to calculate aggregated (excluding the HLA region) trans-scores for gene expression in blood. From associations of T1D with aggregated trans-scores, nine putative core genes were identified, of which three-STAT1, CTLA4 and FOXP3-are genes in which variants cause monogenic forms of autoimmune diabetes. Seven of these genes affect the activity of regulatory T cells, and two are involved in immune responses to microbial lipids. Four T1D-associated genomic regions could be identified as master regulators via trans-effects on gene expression. These results support the sparse effector hypothesis and reshape our understanding of the genetic architecture of T1D.