### Mathematics Colloquium

# Michael Stoll

### (Universität Bayreuth)

## "Torsion points on elliptic curves"

** Date: ** |
Mon, September 13, 2010 |

** Time: ** |
17:15 |

** Place: ** |
Research II Lecture Hall |

**Abstract:** Elliptic curves are curves whose set of points carries a natural group
structure. If the curve is defined over an algebraic number field *K*, then
its *K*-rational points form a finitely generated abelian group. In
particular, the torsion subgroup is finite. So it is a natural question which
natural numbers occur as the order of a torsion point on an elliptic curve
over a number field of degree at most *d*. I will report on joint work with
Sheldon Kamienny and William Stein; we determined the set of prime numbers
that occur in this setting when d=4.