Schizophrenia is a genetic disease but there are no common alleles with even moderate effect, all make tiny contributions.
From an evolutionary viewpoint, we can stop imagining we will find the responsible genes, and instead ask a different question: Why do so many different alleles contribute to the same kind of pathological phenotype? Put differently, we can look for traits pushed fast and hard to extremes close to a "cliff edge"
Nesse, RM: Cliff-edged fitness functions and the persistence of schizophrenia (commentary). Behavioral and Brain Sciences, 2004.
For a wonderful review of evolutionary ideas about schizophrenia, see this article by vanDongen.