Birational maps and Nori motives (Q6191245)

Summary: The monograph by \textit{A. Huber} and \textit{S. Müller-Stach} [Periods and Nori motives. Cham: Springer (2017; Zbl 1369.14001), pp. 207--232] contains a systematic exposition of Nori motives that were developed and studied as the ``universal (co)homology theory'' of algebraic varieties (or schemes), according to the prophetic vision of A. Grothendieck. Since then, some research was dedicated to applications of Nori motives in various domains of algebraic geometry: geometries in characteristic 1 (see the work of \textit{J. F. Lieber} et al. [Lond. Math. Soc. Lect. Note Ser. 473, 147--227 (2022; Zbl 1489.14005)] and \textit{Y. I. Manin} and \textit{M. Marcolli} [Contemp. Math. 744, 27--56 (2020; Zbl 1504.14007)]), absolute Galois group (see the article of \textit{Y. I. Manin} and \textit{M. Marcolli} [SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 038, 52 p. (2020; Zbl 1505.11095)]), persistence formalism (see \textit{Y. I. Manin} and \textit{M. Marcolli} [Math. Comput. Sci. 14, No. 1, 77--102 (2020; Zbl 1464.18002)]). In this chapter, we sketch an approach to the problems of equivariant birational geometry developed by \textit{M. Kontsevich} and \textit{Y. Tschinkel} [Invent. Math. 217, No. 2, 415--432 (2019; Zbl 1420.14030)], where Burnside invariants were introduced. We are making explicit the role of Nori constructions in this environment. For the entire collection see [Zbl 1519.57002].