Characteristic classes of proalgebraic varieties and motivic measures (Q422115)

Let \(I\) be a directed set and let \(\{X_i\}_{i\in I}\) be a projective system of complex algebraic varieties. The projective limit of the system is called a proalgebraic variety. In this paper, based on Fulton-MacPherson bivariant theory [\textit{W. Fulton}, Intersection theory. 2nd ed. Berlin: Springer (1998; Zbl 0885.14002)], the author formulates a general theory of characteristic classes of proalgebraic varieties as a natural extension of the theories of characteristic classes of singular varieties. He also shows that his approach leads one to the notion of motivic measure.