Parametrization of virtually $K$-rational Drinfeld modules of rank two
| Autor: | Yoshiaki Okumura |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Functiones et Approximatio Commentarii Mathematici. 65 |
| ISSN: | 0208-6573 |
| Popis: | For an extension $K/\mathbb{F}_q(T)$ of the rational function field over a finite field, we introduce the notion of virtually $K$-rational Drinfeld modules as a function field analogue of $\mathbb{Q}$-curves. Our goal in this article is to prove that all virtually $K$-rational Drinfeld modules of rank two with no complex multiplication are parametrized up to isogeny by $K$-rational points of a quotient curve of the Drinfeld modular curve $Y_0(\mathfrak{n})$ with some square-free level $\mathfrak{n}$. This is an analogue of Elkies' well-known result on $\mathbb{Q}$-curves. Comment: 12 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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