Connected components of the moduli space of L-parameters
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914770547900416 |
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| author | Cotner, Sean |
| author_facet | Cotner, Sean |
| contents | Recently, in order to formulate a categorical version of the local Langlands correspondence, several authors have constructed moduli spaces of $\mathbf{Z}[1/p]$-valued L-parameters for $p$-adic groups. The connected components of these spaces over various $\mathbf{Z}[1/p]$-algebras $R$ are conjecturally related to blocks in categories of $R$-representations of $p$-adic groups. Dat-Helm-Kurinczuk-Moss described the components when $R$ is an algebraically closed field and gave a conjectural description when $R = \overline{\mathbf{Z}}[1/p]$. In this paper, we prove a strong form of this conjecture applicable to any integral domain $R$ over $\overline{\mathbf{Z}}[1/p]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connected components of the moduli space of L-parameters Cotner, Sean Number Theory Algebraic Geometry Representation Theory 11F80, 20G35 Recently, in order to formulate a categorical version of the local Langlands correspondence, several authors have constructed moduli spaces of $\mathbf{Z}[1/p]$-valued L-parameters for $p$-adic groups. The connected components of these spaces over various $\mathbf{Z}[1/p]$-algebras $R$ are conjecturally related to blocks in categories of $R$-representations of $p$-adic groups. Dat-Helm-Kurinczuk-Moss described the components when $R$ is an algebraically closed field and gave a conjectural description when $R = \overline{\mathbf{Z}}[1/p]$. In this paper, we prove a strong form of this conjecture applicable to any integral domain $R$ over $\overline{\mathbf{Z}}[1/p]$. |
| title | Connected components of the moduli space of L-parameters |
| topic | Number Theory Algebraic Geometry Representation Theory 11F80, 20G35 |
| url | https://arxiv.org/abs/2404.16716 |