Fu, Lie; Nguyen, Manh Toan

Orbifold Products for Higher \(K\)-Theory and Motivic Cohomology

Doc. Math. 24, 1769-1810 (2019)
DOI: 10.25537/dm.2019v24.1769-1810
Communicated by Thomas Geisser

Summary

Due to the work of many authors in the last decades, given an algebraic orbifold (smooth proper Deligne-Mumford stack with trivial generic stabilizer), one can construct its orbifold Chow ring and orbifold Grothendieck ring, and relate them by the orbifold Chern character map, generalizing the fundamental work of Chen-Ruan on orbifold cohomology. In this paper, we extend this theory naturally to higher Chow groups and higher algebraic \(K\)-theory, mainly following the work of Jarvis-Kaufmann-Kimura and Edidin-Jarvis-Kimura.

Mathematics Subject Classification

19E08, 19E15, 14C15, 55N32

Keywords/Phrases

orbifold cohomology, \(K\)-theory, motivic cohomology, Chow rings, hyper-Kähler resolution

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Affiliation

Fu, Lie
Institut Camille Jordan, Université Claude Bernard Lyon 1, 69100, Villeurbanne, France \& IMAPP, Radboud University, Netherlands
Nguyen, Manh Toan
Institut für Mathematik, Universität Osnabrück, Germany

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