The integral (log) cotangent complex of extensions of valued fields
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866918425564020736 |
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| author | Maex, Michaël |
| author_facet | Maex, Michaël |
| contents | Let $(L, v_L) / (K, v_K)$ be a finite or purely transcendental extension of real valued fields. We construct the associated integral cotangent and log cotangent complexes in terms of a MacLane-Vaquié chain approximating $v_L$. This leads to explicit formulas for associated invariants such as the (absolute) (log) different, weight norm and Kähler norm. As a corollary of our methods we obtain strong control of the higher homology of the integral (log) cotangent complex, generalizing an important result of Gabber and Ramero to the logarithmic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01992 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The integral (log) cotangent complex of extensions of valued fields Maex, Michaël Algebraic Geometry 12J20 (primary) 11S15, 14G22 (secondary) Let $(L, v_L) / (K, v_K)$ be a finite or purely transcendental extension of real valued fields. We construct the associated integral cotangent and log cotangent complexes in terms of a MacLane-Vaquié chain approximating $v_L$. This leads to explicit formulas for associated invariants such as the (absolute) (log) different, weight norm and Kähler norm. As a corollary of our methods we obtain strong control of the higher homology of the integral (log) cotangent complex, generalizing an important result of Gabber and Ramero to the logarithmic setting. |
| title | The integral (log) cotangent complex of extensions of valued fields |
| topic | Algebraic Geometry 12J20 (primary) 11S15, 14G22 (secondary) |
| url | https://arxiv.org/abs/2604.01992 |