Semisimplicity of the Galois representations attached to Drinfeld modules over fields of ``finite characteristics'' (Q1814233)

The classical finiteness theorem for the isogenies of abelian varieties over functional fields of positive characteristic [\textit{Yu. G. Zarkhin} in Funct. Anal. Appl. 8 (1974), 301-303 (1975); translation from Funkts. Anal. Prilozh. 8, No. 4, 31-34 (1974; Zbl 0324.14009)] is extended to the Drinfeld modules. The proof uses a notion of modular height for the Drinfeld es. As a corollary it is proved (along the usual lines) the semi-simplicity for the Tate modules of Drinfeld modules.