There will be talks in April and May 2026. The seminar will take place in Aula INdAM at 12.
2026.04.24. Valentijn Karemaker (University of Amsterdam)
Arithmetic invariants of supersingular abelian varieties
We will study the moduli space of abelian varieties in characteristic p and in particular its supersingular locus S_g. We will show when this locus is geometrically irreducible, thereby solving a “class number one problem” or “Gauss problem” for the number of irreducible components; and when a polarised abelian variety is determined by its p-divisible group, solving a Gauss problem for central leaves, which are the loci consisting of points whose associated p-divisible groups are geometrically isomorphic. Furthermore, we will discuss Oort's conjecture, which states that all generic points of S_g have automorphism group {+/- 1}.
This is based on joint works with Ibukiyama and Yu.
2026.05.08. Diana Mocanu (Max Planck Institute of Mathematics)
Local points on twists of X(p)
Let E be a rational elliptic curve and p an odd prime. The modular curve X_E^{-}(p) parametrizes elliptic curves with p-torsion modules anti-symplectically isomorphic to E[p]. In this talk, I present my recent work with Nuno Freitas on a complete classification for when these curves admit points everywhere locally.
We will see two applications of this result. Firstly, I will show how to construct counterexamples to Hasse’s principle of the shape X_E^{-}(p) for fixed E and infinitely many primes p. Secondly, I will present an application of the modular method together with our results to prove certain generalized Fermat equations have no non-trivial coprime solutions.
2026.05.15. Anna von Pippich (University of Konstanz)
TBA
2026.05.22. Daniele Bartoli (Università di Perugia)
TBA
2026.06.05. Giacomo Micheli (University of South Florida)
TBA
Past Events