Notes on Milnor-Witt K-theory
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917027672752128 |
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| author | Déglise, Frédéric |
| author_facet | Déglise, Frédéric |
| contents | These notes develop the foundations of Milnor-Witt K-theory for fields of arbitrary characteristic, without any perfectness assumptions. Extending the work of Morel and Feld, we establish all functorial properties of Milnor-Witt K-theory with careful attention to twists. A main new contribution is the computation of transfers in the general, in particular inseparable, case using Grothendieck (differential) trace maps. The results provide a complete framework for the functoriality axioms of Milnor-Witt modules and form the basis for an upcoming work on Chow-Witt groups with Niels Feld and Fangzhou Jin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18609 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Notes on Milnor-Witt K-theory Déglise, Frédéric Algebraic Geometry Algebraic Topology K-Theory and Homology 19D45, 14F42, 11E81, 11E39, 19E99, 11E04, 16S10 These notes develop the foundations of Milnor-Witt K-theory for fields of arbitrary characteristic, without any perfectness assumptions. Extending the work of Morel and Feld, we establish all functorial properties of Milnor-Witt K-theory with careful attention to twists. A main new contribution is the computation of transfers in the general, in particular inseparable, case using Grothendieck (differential) trace maps. The results provide a complete framework for the functoriality axioms of Milnor-Witt modules and form the basis for an upcoming work on Chow-Witt groups with Niels Feld and Fangzhou Jin. |
| title | Notes on Milnor-Witt K-theory |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology 19D45, 14F42, 11E81, 11E39, 19E99, 11E04, 16S10 |
| url | https://arxiv.org/abs/2305.18609 |