Differential Galois groups, specializations and Matzat's conjecture
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916449045446656 |
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| author | Feng, Ruyong Wibmer, Michael |
| author_facet | Feng, Ruyong Wibmer, Michael |
| contents | We study families of linear differential equations parametrized by an algebraic variety $\mathcal{X}$ and show that the set of all points $x\in \mathcal{X}$, such that the differential Galois group at the generic fibre specializes to the differential Galois group at the fibre over $x$, is Zariski dense in $\mathcal{X}$. As an application, we prove Matzat's conjecture in full generality: The absolute differential Galois group of a one-variable function field over an algebraically closed field of characteristic zero is a free proalgebraic group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_01581 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Differential Galois groups, specializations and Matzat's conjecture Feng, Ruyong Wibmer, Michael Algebraic Geometry Commutative Algebra 14L15, 34M50, 12H05 We study families of linear differential equations parametrized by an algebraic variety $\mathcal{X}$ and show that the set of all points $x\in \mathcal{X}$, such that the differential Galois group at the generic fibre specializes to the differential Galois group at the fibre over $x$, is Zariski dense in $\mathcal{X}$. As an application, we prove Matzat's conjecture in full generality: The absolute differential Galois group of a one-variable function field over an algebraically closed field of characteristic zero is a free proalgebraic group. |
| title | Differential Galois groups, specializations and Matzat's conjecture |
| topic | Algebraic Geometry Commutative Algebra 14L15, 34M50, 12H05 |
| url | https://arxiv.org/abs/2209.01581 |