NON-RATIONALITY OF PROJECTIVE APPROXIMATIONS FOR CLASSIFYING SPACES

抄録

Let BG be the classifying space of an algebraic group G over a subfield k of the complex numbers C. We compute a new stable birational invariant defined by Benoist and Ottem [Duke Math. J. 170 (2021), 2719–2753] as the difference of two coniveau filtrations of a smooth projective (Ekedahl) approximation X of BG×P^∞. Then we show (without and with the unramified cohomology) that in many cases X are not stable rational.