Manin's proof of the Mordell conjecture over function fields
The author rediscusses Manin's proof of Mordell's conjecture over function fields [see \textit{Yu. I. Manin}, Transl., Ser. 2, Am. Math. Soc. 50, 189-234 (1966); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 27, 1395-1440 (1963; Zbl 0166.169)] in modern language. In this process he also fills a gap in Manin's proof of the theorem of the kernel. It is interesting to note that the way in which he fills this gap makes Manin's proof of the Mordell conjecture over function fields completely algebraic.
Mordell's conjecture over function fields
scientific article; zbMATH DE number 4204538