A counter-example by Yagita

Abstract

According to a 2018 preprint by Nobuaki Yagita, the conjecture on a relationship between [Formula: see text]- and Chow theories for a generically twisted flag variety of a split semisimple algebraic group [Formula: see text], due to the author, fails for [Formula: see text] the spinor group [Formula: see text]. Yagita’s tools include a Brown–Peterson version of algebraic cobordism, ordinary and connective Morava [Formula: see text]-theories, as well as Grothendieck motives related to various cohomology theories over fields of characteristic [Formula: see text]. We provide a proof using only the [Formula: see text]- and Chow theories themselves and extend the (slightly modified) example to arbitrary characteristic.