An analogue of the Milnor conjecture for the de Rham-Witt complex in characteristic 2
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913860190994432 |
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| author | Dotto, Emanuele |
| author_facet | Dotto, Emanuele |
| contents | We describe the modulo $2$ de Rham-Witt complex of a field of characteristic $2$, in terms of the powers of the augmentation ideal of the $\mathbb{Z}/2$-geometric fixed points of real topological restriction homology TRR. This is analogous to the conjecture of Milnor, proved by Kato for fields of characteristic $2$, which describes the modulo $2$ Milnor K-theory in terms of the powers of the augmentation ideal of the Witt group of symmetric forms. Our proof provides a somewhat explicit description of these objects, as well as a calculation of the homotopy groups of the geometric fixed points of TRR and of real topological cyclic homology, for all fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02054 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An analogue of the Milnor conjecture for the de Rham-Witt complex in characteristic 2 Dotto, Emanuele Algebraic Topology K-Theory and Homology Number Theory Primary 19D55, 11E81, 13F35, Secondary 55P91, 14F30, 19D45 We describe the modulo $2$ de Rham-Witt complex of a field of characteristic $2$, in terms of the powers of the augmentation ideal of the $\mathbb{Z}/2$-geometric fixed points of real topological restriction homology TRR. This is analogous to the conjecture of Milnor, proved by Kato for fields of characteristic $2$, which describes the modulo $2$ Milnor K-theory in terms of the powers of the augmentation ideal of the Witt group of symmetric forms. Our proof provides a somewhat explicit description of these objects, as well as a calculation of the homotopy groups of the geometric fixed points of TRR and of real topological cyclic homology, for all fields. |
| title | An analogue of the Milnor conjecture for the de Rham-Witt complex in characteristic 2 |
| topic | Algebraic Topology K-Theory and Homology Number Theory Primary 19D55, 11E81, 13F35, Secondary 55P91, 14F30, 19D45 |
| url | https://arxiv.org/abs/2405.02054 |