Vendredi 15 Avril
Heure: 
10:30  11:30 
Lieu: 
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13 
Résumé: 
Géométrie Arithmétique et Motivique  Finiteness of pointed families of varieties  
Description: 
Ariyan Javanpeykar Shafarevich proved that the set of nonisotrivial elliptic curves over a fixed base curve B is finite, and conjectured a similar statement for higher genus curves in his 1962 ICM paper. This conjecture was proven by ArakelovParshin in the 70's. Subsequently, in 1983, Faltings investigated the analogue of these finiteness theorems for nonisotrivial abelian schemes, and showed that one can no longer expect finiteness. The reason is simple: the moduli space of abelian varieties contains product subvarieties. However, combining Faltings's work on the boundedness of the moduli space of families of abelian varieties with Grothendieck's work on Tate modules, one can show the finiteness of pointed families of abelian varieties: For every smooth variety B, every point b, every principally polarized abelian variety A, the set of Bisomorphism classes of principally polarized abelian schemes X&gt;B with X_b = A is finite. This finiteness statement (which one may refer to as the "pointed Shafarevich conjecture") was extended by Deligne to the larger context of moduli spaces with a quasifinite period map (e.g., moduli of polarized K3 surfaces, polarized hyperkaehler varieties, or polarized CYvarieties).&nbsp; But there are moduli spaces of varieties of general type which aren't known to have a quasifinite period map. Is there a similar finiteness result for pointed families of such varieties? In joint work with Steven Lu, Ruiran Sun, and Kang Zuo, we give a positive answer to this question for the moduli stack of varieties with ample canonical bundle. 
Heure: 
11:00  12:00 
Lieu: 
mode hybride B405 et lien bbb 
Résumé: 
MB  Towards a new mathematical model of the visual cycle  
Description: 
Luca Alasio 

