LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

Galois criterion for torsion points of Drinfeld modules

Photo by kaleidico from unsplash

In this paper, we formulate the Drinfeld module analogue of a question raised by Lang and studied by Katz on the existence of rational points on abelian varieties over number… Click to show full abstract

In this paper, we formulate the Drinfeld module analogue of a question raised by Lang and studied by Katz on the existence of rational points on abelian varieties over number fields. Given a maximal ideal [Formula: see text] of [Formula: see text], the question essentially asks whether, up to isogeny, a Drinfeld module [Formula: see text] over [Formula: see text] contains a rational [Formula: see text]-torsion point if the reduction of [Formula: see text] at almost all primes of [Formula: see text] contains a rational [Formula: see text]-torsion point. Similar to the case of abelian varieties, we show that the answer is positive if the rank of the Drinfeld module is 2, but negative if the rank is 3. Moreover, for rank 3 Drinfeld modules we classify those cases where the answer is positive.

Keywords: drinfeld module; torsion; drinfeld modules; formula see; see text

Journal Title: International Journal of Number Theory
Year Published: 2021

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.