A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks

A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks

We develop a motivic cohomology theory, representable in the Voevodsky's triangulated category of motives, for smooth separated Deligne-Mumford stacks and show that the resulting higher Chow groups are canonically isomorphic to the higher $K$-theory of such stacks. This generalises the Grothend...

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Hauptverfasser: Choudhury, Utsav, Deshmukh, Neeraj, Hogadi, Amit
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Algebraic Geometry
Mathematics - K-Theory and Homology
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Zusammenfassung:We develop a motivic cohomology theory, representable in the Voevodsky's triangulated category of motives, for smooth separated Deligne-Mumford stacks and show that the resulting higher Chow groups are canonically isomorphic to the higher $K$-theory of such stacks. This generalises the Grothendieck-Riemann-Roch theorem to the category of smooth Deligne-Mumford stacks.
DOI:10.48550/arxiv.2412.05071