We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On isogeny characters of Drinfeld modules of rank two.
- Authors
Ishii, Shun
- Abstract
In this paper, we study cyclic torsion subgroups of Drinfeld F q [ T ] -modules of rank two over F q (T) via isogeny characters associated to them. Among other things, we prove that such Drinfeld F q [ T ] -modules do not have a cyclic p -torsion subgroup defined over F q (T) under various assumptions, where p is a maximal ideal of F q [ T ] . For example, we show that any Drinfeld F q [ T ] -module of rank two over F q (T) which has good reduction at every finite place of F q (T) does not have a p -isogeny defined over F q (T) , where p is a maximal ideal of F q [ T ] with deg (p) > q . We also show that the set of K-rational points of Drinfeld modular curve X 0 (p) only consists of cusps when deg (p) is equal to four. These results partially generalize preceding works by Pál and Armana, respectively.
- Subjects
DRINFELD modules; TORSION; TORSION theory (Algebra); POINT set theory
- Publication
Mathematische Zeitschrift, 2022, Vol 301, Issue 1, p455
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-021-02921-5