The study cited in this blog shows that small changes in IQ have a much bigger impact on incarceration rates than do small changes in socioeconomic status.  (Of course, having a higher IQ might just stop you from getting caught rather than reducing the amount of crime you engage in.)

If it turns out that brain fitness programs such as the duel-N-back succeed in increasing IQ then massive use of duel-N-back by students in dangerous neighborhoods might do much to reduce crime.