I have been working with perfect separation in logistic regression, and I have been assessing models with the AUC statistic. I was wondering what affect perfect separation has on the AUC. My own understanding is that perfect separation via inflated coefficients will reduce the AUC because it results in a lowering of the True Positive Rate, whilst the False Positive rate remains unaffected, but I might have misunderstood something. Can anyone explain the relation between the two?