Degeneration Theorems of Connes and Feigin--Tsygan Type in Mixed Characteristic, with q-Analogues
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910218879762432 |
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| author | Matsumoto, Keiho |
| author_facet | Matsumoto, Keiho |
| contents | We prove mixed-characteristic analogues of the Connes and Feigin--Tsygan degeneration theorem. Let $W=W(k)$ be the Witt vectors of a perfect field of characteristic $p>0$. For a smooth proper variety $X$ over $W$, the de Rham-to-$\HP$ spectral sequence is split degenerate under the small-dimension hypothesis $dim(X/W)<p-1$. More generally, if $X$ is smooth and proper over the ring of integers $O_K$ of a finite extension of $\mathrm{Frac}(W)$ with ramification index $e$, we prove the corresponding split degeneration under $2e dim(X/O_K)<p-1$. Under the same ramification hypothesis, we also prove split degeneration of the $Ainf$-to-$TP$ spectral sequence. Finally, after inverting an explicit factorial, we obtain a topological $q$-de Rham analogue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14286 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Degeneration Theorems of Connes and Feigin--Tsygan Type in Mixed Characteristic, with q-Analogues Matsumoto, Keiho Algebraic Geometry We prove mixed-characteristic analogues of the Connes and Feigin--Tsygan degeneration theorem. Let $W=W(k)$ be the Witt vectors of a perfect field of characteristic $p>0$. For a smooth proper variety $X$ over $W$, the de Rham-to-$\HP$ spectral sequence is split degenerate under the small-dimension hypothesis $dim(X/W)<p-1$. More generally, if $X$ is smooth and proper over the ring of integers $O_K$ of a finite extension of $\mathrm{Frac}(W)$ with ramification index $e$, we prove the corresponding split degeneration under $2e dim(X/O_K)<p-1$. Under the same ramification hypothesis, we also prove split degeneration of the $Ainf$-to-$TP$ spectral sequence. Finally, after inverting an explicit factorial, we obtain a topological $q$-de Rham analogue. |
| title | Degeneration Theorems of Connes and Feigin--Tsygan Type in Mixed Characteristic, with q-Analogues |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.14286 |