ANALYSE APPLIQUÉE, ANALYSE SEMI-CLASSIQUE & PHYSIQUE MATHÉMATIQUE, ANALYSE SPECTRALE ET PHYSIQUE MATHÉMATIQUE (SÉMINAIRE TOURNANT), CHAIRE FSMP NADER MASMOUDI, CONOMIE ET MATHÉMATIQUES, DISCUSSIONS MATHÉMATIQUES FRANCO-MAROCAINES, EDP & PHYSIQUE MATHÉMATIQUE, EDP ET CALCUL SCIENTIFIQUE, GROUPE DE TRAVAIL PROBA-STATS, GÉOMÉTRIE ARITHMÉTIQUE ET MOTIVIQUE, IMAGE LAGA-LIPN-L2TI, MB, MODÉLISATION ET CALCUL SCIENTIFIQUE, PM - EDP, PROTECTION DE L'INFORMATION, QUATIONS AUX DÉRIVÉES PARTIELLES NON-LINÉAIRES, SURFACES K3, THÉORIE ERGODIQUE ET SYSTÈMES DYNAMIQUES, TOPOLOGIE ALGÉBRIQUE, VIDÉO-SÉMINAIRE EDP BERKELEY BONN PARIS-NORD, VIDÉO-SÉMINAIRE EDP BERKELEY BONN PARIS-NORD ZURICH

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-&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 quasi-finite period map (e.g., moduli of polarized K3 surfaces, polarized hyperkaehler varieties, or polarized CY-varieties).&nbsp; 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.

Vendredi 15 Avril