Periods of generic torsors of groups of multiplicative type (Q392226)

The main result of this paper gives five equivalent ways to compute the period of a generic torsor of a smooth group of multiplicative type. The author also proves that the period of \(Q\) is divisible by the periods of \(T\) and \(W\), where \(Q\) is a group of multiplicative type, \(T \subset Q\) is a maximal torus, and \(W = Q/T\) is the maximal finite quotient. In addition, given a finite subgroup \(Z \subset Q\), the paper contains a cohomological condition which implies that the period of \(Q\) divides the exponent of \(Z\).