$p$-adic non-abelian Hodge theory for curves via moduli stacks
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911769722617856 |
|---|---|
| author | Heuer, Ben Xu, Daxin |
| author_facet | Heuer, Ben Xu, Daxin |
| contents | For a smooth projective curve $X$ over $\mathbb C_p$ and any reductive group $G$, we show that the moduli stack of $G$-Higgs bundles on $X$ is a twist of the moduli stack of v-topological $G$-bundles on $X_v$ in a canonical way. We explain how a choice of an exponential trivialises this twist on points. This yields a geometrisation of Faltings' $p$-adic Simpson correspondence for $X$, which we recover as a homeomorphism between the points of moduli spaces. We also show that our twisted isomorphism sends the stack of $p$-adic representations of $π_1(X)$ to an open substack of the stack of semi-stable Higgs bundles of degree $0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01365 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $p$-adic non-abelian Hodge theory for curves via moduli stacks Heuer, Ben Xu, Daxin Algebraic Geometry 14D22, 14G22, 14D10, 14F30 For a smooth projective curve $X$ over $\mathbb C_p$ and any reductive group $G$, we show that the moduli stack of $G$-Higgs bundles on $X$ is a twist of the moduli stack of v-topological $G$-bundles on $X_v$ in a canonical way. We explain how a choice of an exponential trivialises this twist on points. This yields a geometrisation of Faltings' $p$-adic Simpson correspondence for $X$, which we recover as a homeomorphism between the points of moduli spaces. We also show that our twisted isomorphism sends the stack of $p$-adic representations of $π_1(X)$ to an open substack of the stack of semi-stable Higgs bundles of degree $0$. |
| title | $p$-adic non-abelian Hodge theory for curves via moduli stacks |
| topic | Algebraic Geometry 14D22, 14G22, 14D10, 14F30 |
| url | https://arxiv.org/abs/2402.01365 |