Vendredi 15 Avril

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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 non-isotrivial 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 Arakelov-Parshin in the 70's. Subsequently,
in 1983, Faltings investigated the analogue of these finiteness theorems
for non-isotrivial 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
B-isomorphism classes of principally polarized abelian schemes X->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 quasi-finite period map (e.g., moduli of
polarized K3 surfaces, polarized hyperkaehler varieties, or polarized
CY-varieties).  But there are moduli spaces of varieties of general type
which aren't known to have a quasi-finite 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