The group of congruence coefficients of a canonical quadratic form and stable rationality of the \(PSO\) variety
One of the basic problems in studying the geometric properties of varieties of linear algebraic groups is the problem of rationality. There is Platonov's conjecture of \(K\)-rationality for the variety of a semisimple connected algebraic group \(G\) defined over an arbitrary field \(K\). The following two statements are the main results of the present paper: Theorem 1. Let \(f\) be a canonical quadratic form defined over an arbitrary field \(K\), \(\text{char } K=2\). Then the group \(PSO (f)\) is stably rational over \(K\). Theorem 2. Let \(G\) be an arbitrary compact semisimple \(\mathbb{R}\)-defined algebraic group that does not contain factors of types \(E_i\), \(i=6, 7, 8\). Then the group variety \(G\) is stably rational over \(\mathbb{R}\).
scientific article; zbMATH DE number 771976