Abstract:

Rationality problems for conic bundles have been well studied over surfaces. In this talk, we generalize an etale cohomology diagram from the case of conic bundles to Brauer-Severi surface bundles over rational 3-folds . We use this generalization to prove a sufficient condition for a Brauer-Severi surface bundle to be not stably Rational. We also give an example satisfying these sufficient conditions.