| Autor: |
Feng, Ruyong, Guo, Zewang, Lu, Wei |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We prove a differential analogue of Hilbert's irreducibility theorem. Let $\mathcal{L}$ be a linear differential operator with coefficients in $C(\mathbb{X})(x)$ that is irreducible over $\overline{C(\mathbb{X})}(x)$, where $\mathbb{X}$ is an irreducible affine algebraic variety over an algebraically closed field $C$ of characteristic zero. We show that the set of $c\in \mathbb{X}(C)$ such that the specialized operator $\mathcal{L}^c$ of $\mathcal{L}$ remains irreducible over $C(x)$ is Zariski dense in $\mathbb{X}(C)$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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