Tuesday, July 2, 2019 - 13:15
Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 006, Haus 3, Erdgeschoss
Forschungsseminar Arithmetische Geometrie
Prof. Jürg Kramer / Prof. Thomas Krämer
It is classically known that a singular modulus (a j-invariant of a CM elliptic curve) is an algebraic integer. Habegger (2015) proved that at most finitely many singular moduli are units, answering a question of Masser (2011). However, his argument, being non-effective, did not imply any bound for the size of these "singular units". I will report on a recent work with Philipp Habegger and Lars Kühne, where we prove that singular units do not exist at all. First, we bound the discriminant of any singular unit by 10^{15}. Next, we rule out the remaining singular units using computer-assisted arguments.
submitted by Marion Thomma (thomma@math.hu-berlin.de, 2093-5815)