Tropical analogs of Milnor $K$-groups and tropicalizations of Zariski-Riemann spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866913201043537920 |
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| author | Mikami, Ryota |
| author_facet | Mikami, Ryota |
| contents | As a step of a tropical approach to problems on algebraic classes of cohomology groups (such as the Hodge conjecture), in this paper, we introduce tropical analogs of (rational) Milnor $K$-groups, and prove the existence of the Gersten resolution of their Zariski sheafification. Our result will be used to prove a tropical analog of the Hodge conjecture for smooth algebraic varieties over trivially valued fields in a subsequent paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_04677 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Tropical analogs of Milnor $K$-groups and tropicalizations of Zariski-Riemann spaces Mikami, Ryota Algebraic Geometry As a step of a tropical approach to problems on algebraic classes of cohomology groups (such as the Hodge conjecture), in this paper, we introduce tropical analogs of (rational) Milnor $K$-groups, and prove the existence of the Gersten resolution of their Zariski sheafification. Our result will be used to prove a tropical analog of the Hodge conjecture for smooth algebraic varieties over trivially valued fields in a subsequent paper. |
| title | Tropical analogs of Milnor $K$-groups and tropicalizations of Zariski-Riemann spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2009.04677 |