What Did Judas Betray?

The Gospels agree that Judas Iscariot betrayed Jesus, even if they don't agree on why he did it. But is their view about *what* he did plausible? That he told the authorities where they could find Jesus without any crowds around? There are, in fact, reasons for thinking that Judas did something far more sinister, that he revealed a key teaching of Jesus gave to his closest followers but he did not proclaim in public. Did Judas reveal a secret teaching that led to Jesus' crucifixion?