zbMATH — the first resource for mathematics

On a result of Imin Chen. (Sur un rĂ©sultat d’Imin Chen.) (French) Zbl 0968.14024
Given a prime \(p\), a result of I. Chen [Proc. Lond. Math. Soc. (3) 77, 1-38 (1998; Zbl 0903.11019)] shows that there is an isogeny between Jacobians of modular curves associated to subgroups of \(GL_2 (\mathbb F_p)\). In this paper the authors generalize this result by considering objects with actions by \(GL_2 (\mathbb F)\), with \(\mathbb F\) an arbitrary finite field, in more general additive categories.

14K02 Isogeny
14H40 Jacobians, Prym varieties
11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
Full Text: DOI