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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.05071 |
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| _version_ | 1866912401598709760 |
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| author | Choudhury, Utsav Deshmukh, Neeraj Hogadi, Amit |
| author_facet | Choudhury, Utsav Deshmukh, Neeraj Hogadi, Amit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks Choudhury, Utsav Deshmukh, Neeraj Hogadi, Amit Algebraic Geometry K-Theory and Homology 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. |
| title | A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2412.05071 |