The relative GAGA Theorem and an application to the analytic mapping stacks
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909994099671040 |
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| author | Wang, Qixiang |
| author_facet | Wang, Qixiang |
| contents | We prove a relative GAGA theorem for perfect and pseudo-coherent complexes in non-archimedean analytic geometry, allowing bases given by Fredholm analytic rings, including those associated from affinoid perfectoid spaces. This answers a question raised in \cite{heuer2024padicnonabelianhodgetheory}. As an application, we show that for a proper scheme \(X\) and an Artin stack \(Y\) with suitable conditions, the analytification of the algebraic mapping stack \(\mathrm{Map}(X,Y)\) agrees with the intrinsic analytic mapping stack \(\mathrm{Map}(X^{\mathrm{an}},Y^{\mathrm{an}})\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12299 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The relative GAGA Theorem and an application to the analytic mapping stacks Wang, Qixiang Algebraic Geometry We prove a relative GAGA theorem for perfect and pseudo-coherent complexes in non-archimedean analytic geometry, allowing bases given by Fredholm analytic rings, including those associated from affinoid perfectoid spaces. This answers a question raised in \cite{heuer2024padicnonabelianhodgetheory}. As an application, we show that for a proper scheme \(X\) and an Artin stack \(Y\) with suitable conditions, the analytification of the algebraic mapping stack \(\mathrm{Map}(X,Y)\) agrees with the intrinsic analytic mapping stack \(\mathrm{Map}(X^{\mathrm{an}},Y^{\mathrm{an}})\). |
| title | The relative GAGA Theorem and an application to the analytic mapping stacks |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.12299 |