Can smoking pot as a teenager cause schizophrenia in adulthood?

Short answer: no.

An interesting editorial was just published summarizing research on the potential link between marijuana use and schizophrenia. Here's a quick breakdown for curious patients.

1. Adolescent marijuana usage doesn't cause schizophrenia. There is no strong scientific evidence for this.
2. Marijuana is likely used as self-medication after onset of symptoms because it can decrease negative and cognitive symptoms. However, it has adverse effects that outreach the benefits. It increases positive symptoms and is correlated with a poorer long-term prognosis. 
3. It's likely that use during adolescence can be a risk factor to people who already have a vulnerability to developing schizophrenia (IE a family history of it). 

Why is adolescent use more important to study than adult use in this context? Because the brain is changing rapidly during adolescence especially in areas involved in schizophrenia and where there are high densities of the receptors that marijuana binds to.

Reference 
Hill, M. N. (2014). Clearing the smoke: What do we know about adolescent cannabis use and schizophrenia? J. Psychiatry Neurosci. 39, 75–77. (Free full text available.)