Splitting and making explicit the de Rham complex of the Drinfeld space
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| Format: | Preprint |
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2024
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| _version_ | 1866915748195074048 |
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| author | Breuil, Christophe Qian, Zicheng |
| author_facet | Breuil, Christophe Qian, Zicheng |
| contents | Let $p$ be a prime number, $K$ a finite extension of $\mathbb{Q}_p$ and $n$ an integer $\geq 2$. We completely and explicitly describe the global sections $Ω^\bullet$ of the de Rham complex of the Drinfeld space over $K$ in dimension $n-1$ as a complex of (duals of) locally $K$-analytic representations of $\mathrm{GL}_n(K)$. Using this description, we construct an explicit section in the derived category of (duals of) finite length admissible locally $K$-analytic representations of $\mathrm{GL}_n(K)$ to the canonical morphism of complexes $Ω^\bullet \twoheadrightarrow H^{n-1}(Ω^\bullet)[-(n-1)]$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_06651 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Splitting and making explicit the de Rham complex of the Drinfeld space Breuil, Christophe Qian, Zicheng Number Theory Representation Theory Let $p$ be a prime number, $K$ a finite extension of $\mathbb{Q}_p$ and $n$ an integer $\geq 2$. We completely and explicitly describe the global sections $Ω^\bullet$ of the de Rham complex of the Drinfeld space over $K$ in dimension $n-1$ as a complex of (duals of) locally $K$-analytic representations of $\mathrm{GL}_n(K)$. Using this description, we construct an explicit section in the derived category of (duals of) finite length admissible locally $K$-analytic representations of $\mathrm{GL}_n(K)$ to the canonical morphism of complexes $Ω^\bullet \twoheadrightarrow H^{n-1}(Ω^\bullet)[-(n-1)]$. |
| title | Splitting and making explicit the de Rham complex of the Drinfeld space |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2407.06651 |