A Voevodsky motive associated to a log scheme
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911764996685824 |
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| author | Shuklin, Georgii |
| author_facet | Shuklin, Georgii |
| contents | For each fs log scheme $(X,\mathcal M_X)$ over a field $k$ we construct a geometrical Voevodsky motive $[X]^{log}\in DM_{gm}(k,\mathbb Q)$. We prove that, for $k=\mathbb C$, the Betti realization of $[X]^{log}$ is the log Betti cohomology of $(X, \mathcal M_X)$. We give applications to motivic tubular neighborhoods, limit motives and the monodromy filtrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03720 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Voevodsky motive associated to a log scheme Shuklin, Georgii Algebraic Geometry For each fs log scheme $(X,\mathcal M_X)$ over a field $k$ we construct a geometrical Voevodsky motive $[X]^{log}\in DM_{gm}(k,\mathbb Q)$. We prove that, for $k=\mathbb C$, the Betti realization of $[X]^{log}$ is the log Betti cohomology of $(X, \mathcal M_X)$. We give applications to motivic tubular neighborhoods, limit motives and the monodromy filtrations. |
| title | A Voevodsky motive associated to a log scheme |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2209.03720 |