Ramification of Tate modules for rank 2 Drinfeld modules

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.

Publication Details

Journal
Tokyo Tech Research Repository (Tokyo Institute of Technology)
Published
2024-12-12
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

Ramification of Tate modules for rank 2 Drinfeld modules

Tokyo Tech Research Repository (Tokyo Institute of Technology)
Algebraic Geometry and Number Theory
article

Ramification of Tate modules for rank 2 Drinfeld modules

article en

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.

Tokyo Tech Research Repository (Tokyo Institute of Technology)
Openalex Percentile: Top 41%
Algebraic Geometry and Number Theory
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Ramification of Tate modules for rank 2 Drinfeld modules · Tokyo Tech Research Repository (Tokyo Institute of Technology) (2024) | TGRS Research Map | TGRS