Tohoku Mathematical Journal
2024
September
SECOND SERIES VOL. 76, NO. 3

Tohoku Math. J.
76 (2024), 445-481

Title RAMIFICATION OF TATE MODULES FOR RANK 2 DRINFELD MODULES

Author Takuya Asayama and Maozhou Huang

(Received September 21, 2022, revised August 30, 2023)
Abstract. In this paper, we study the ramification of extensions of a function field generated by division points of rank 2 Drinfeld modules. Also conductors of certain rank 2 Drinfeld modules are defined as analogues of those for elliptic curves. A calculation of these conductors allows us to show an analogue of Szpiro's conjecture under a certain limited situation.

Mathematics Subject Classification. Primary 11G09; Secondary 11S15, 11S20, 11F80.
Key words and phrases. Drinfeld modules, Herbrand functions, higher ramification subgroups, conductors, Szpiro's conjecture.

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