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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.05051 |
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| _version_ | 1866910048926564352 |
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| author | Merici, Alberto |
| author_facet | Merici, Alberto |
| contents | In this note we will illustrate a method for computing the $π_0$ of the effective log motive of a smooth and proper variety over a perfect field $k$ and show that it is $\mathbf{A}^1$-invariant. We will apply this to compute the first homotopy groups of $\mathbf{P}^1$ to show that the stripping functor from log motivic sheaves to (usual) Nisnevich sheaves with transfers is fully faithful. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some computations in the heart of the homotopy t-structure on logarithmic motives Merici, Alberto Algebraic Geometry In this note we will illustrate a method for computing the $π_0$ of the effective log motive of a smooth and proper variety over a perfect field $k$ and show that it is $\mathbf{A}^1$-invariant. We will apply this to compute the first homotopy groups of $\mathbf{P}^1$ to show that the stripping functor from log motivic sheaves to (usual) Nisnevich sheaves with transfers is fully faithful. |
| title | Some computations in the heart of the homotopy t-structure on logarithmic motives |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.05051 |