Computing the cohomology of constructible étale sheaves on curves
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914327993253888 |
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| author | Levrat, Christophe |
| author_facet | Levrat, Christophe |
| contents | We present an explicit expression of the cohomology complex of a constructible sheaf of abelian groups on the small étale site of an irreducible curve over an algebraically closed field, when the torsion of the sheaf is invertible in the field. This expression only involves finite groups, and is functorial in both the curve and the sheaf. In particular, we explain how to compute the Galois action on this complex. We also present an algorithm which computes it and study its complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03283 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computing the cohomology of constructible étale sheaves on curves Levrat, Christophe Algebraic Geometry Number Theory 14F20, 11G20, 11Y16, 03D99 We present an explicit expression of the cohomology complex of a constructible sheaf of abelian groups on the small étale site of an irreducible curve over an algebraically closed field, when the torsion of the sheaf is invertible in the field. This expression only involves finite groups, and is functorial in both the curve and the sheaf. In particular, we explain how to compute the Galois action on this complex. We also present an algorithm which computes it and study its complexity. |
| title | Computing the cohomology of constructible étale sheaves on curves |
| topic | Algebraic Geometry Number Theory 14F20, 11G20, 11Y16, 03D99 |
| url | https://arxiv.org/abs/2306.03283 |