John Voight

Dartmouth


Counting elliptic curves with torsion, and a probabilistic local-global principle


Heilbronn Number Theory Seminar


17th March 2021, 4:00 pm – 5:00 pm
Zoom,


Can we detect torsion of a rational elliptic curve E by looking modulo primes? Well, for almost all primes p, the torsion subgroup E(Q)_tor maps injectively into E(F_p); but the converse statement holds only up to isogeny, by a theorem of Katz. In this talk, we consider a probabilistic refinement for the elliptic curves themselves: if m | #E(F_p) for almost all primes p, what is the probability that m | #E(Q)_tor? We answer this question in a precise way by giving an asymptotic count of rational elliptic curves by height with certain prescribed Galois image.

This is joint work with John Cullinan and Meagan Kenney.






Comments are closed.
css.php