Moduli stacks of quiver connections and non-Abelian Hodge theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909001081421824 |
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| author | Azam, Mahmud Rayan, Steven |
| author_facet | Azam, Mahmud Rayan, Steven |
| contents | In arXiv:2407.11958, a moduli stack parametrizing $I$--indexed diagrams of Higgs bundles over a base stack $X$ was constructed for any finite simplicial set $I$, inspiring speculations about extending the non-Abelian Hodge correspondence to these moduli stacks. In the present work, we formalize the de Rham side of this conjectural extension. We construct moduli stacks parametrizing diagrams of bundles with $λ$--connections over a base prestack $X$, where $λ$ can be a fixed number or a parameter. Taking $λ$ to be $1$ gives a moduli stack parametrizing diagrams of bundles with connection, while taking it to be a parameter gives a version of Simpson's non-Abelian Hodge filtration for digrams of bundles with connection. We show that when $X$ is a smooth and projective scheme over an algebraically closed field $k$ of characteristic $0$, these moduli stacks are algebraic and locally of finite presentation, and have affine diagonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moduli stacks of quiver connections and non-Abelian Hodge theory Azam, Mahmud Rayan, Steven Algebraic Geometry Category Theory Differential Geometry Rings and Algebras Representation Theory 14D20, 14D22, 14D23, 16G20 In arXiv:2407.11958, a moduli stack parametrizing $I$--indexed diagrams of Higgs bundles over a base stack $X$ was constructed for any finite simplicial set $I$, inspiring speculations about extending the non-Abelian Hodge correspondence to these moduli stacks. In the present work, we formalize the de Rham side of this conjectural extension. We construct moduli stacks parametrizing diagrams of bundles with $λ$--connections over a base prestack $X$, where $λ$ can be a fixed number or a parameter. Taking $λ$ to be $1$ gives a moduli stack parametrizing diagrams of bundles with connection, while taking it to be a parameter gives a version of Simpson's non-Abelian Hodge filtration for digrams of bundles with connection. We show that when $X$ is a smooth and projective scheme over an algebraically closed field $k$ of characteristic $0$, these moduli stacks are algebraic and locally of finite presentation, and have affine diagonal. |
| title | Moduli stacks of quiver connections and non-Abelian Hodge theory |
| topic | Algebraic Geometry Category Theory Differential Geometry Rings and Algebras Representation Theory 14D20, 14D22, 14D23, 16G20 |
| url | https://arxiv.org/abs/2512.12188 |