Non-Rationality of Projective Approximations for Classifying Spaces

Key Points

• The aim is to compute and analyze a stable birational invariant of classifying spaces formed by algebraic groups over a subfield.
• Computed a stable birational invariant from coniveau filtrations of a smooth projective approximation of BG × ℙ ∞.
• Analyzed the non-rationality of approximations without and with unramified cohomology.
• Demonstrated that in many cases, the projective approximations X are not stable rational.
• Identified differences in coniveau filtrations that contribute to the assessment of rationality.