On the Local Structure of Mahler Systems
| Autor: | Julien Roques |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | International Mathematics Research Notices. 2021:9937-9957 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnz349 |
| Popis: | This paper is a 1st step in the direction of a better understanding of the structure of the so-called Mahler systems: we classify these systems over the field $\mathscr{H}$ of Hahn series over $\overline{{\mathbb{Q}}}$ and with value group ${\mathbb{Q}}$. As an application of (a variant of) our main result, we give an alternative proof of the following fact: if, for almost all primes $p$, the reduction modulo $p$ of a given Mahler equation with coefficients in ${\mathbb{Q}}(z)$ has a full set of algebraic solutions over $\mathbb{F}_{p}(z)$, then the given equation has a full set of solutions in $\overline{{\mathbb{Q}}}(z)$ (this is analogous to Grothendieck’s conjecture for differential equations). |
| Databáze: | OpenAIRE |
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