BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alice Lin (Harvard University) DTSTART:20250407T200000Z DTEND:20250407T210000Z DTSTAMP:20260423T040044Z UID:NTBU/23 DESCRIPTION:Title: Sh afarevich's conjecture for families of hypersurfaces over function fields< /a>\nby Alice Lin (Harvard University) as part of Boston University Number Theory Seminar\n\nLecture held in CDS Room 365 in Boston University.\n\nA bstract\nShafarevich's conjecture suggests that over a fixed base scheme $ B$\, whether it is the $S$-integers of a number field or a quasiprojective variety\, there should be only finitely many nonisotrivial families of pr ojective varieties of a given type over $B$. For example\, in proving the Mordell Conjecture\, Faltings proved that there are only finitely many fam ilies of principally polarized abelian schemes of a given dimension over t he $S$-integers of a number field. We prove a Shafarevich conjecture for H odge-generic families of hypersurfaces for sufficiently large degree and d imension over a complex quasiprojective base. The argument follows a "boun dedness and rigidity" structure to show that the space of such families is finite. For boundedness\, the key input is a new result of Bakker\, Brune barbe\, and Tsimerman about the ampleness of the Griffiths line bundle for quasifinite period mappings. For rigidity\, we use a Hodge-theoretic form ulation due to Peters.\n\nThis is joint work with Philip Engel and Salim T ayou.\n LOCATION:https://researchseminars.org/talk/NTBU/23/ END:VEVENT END:VCALENDAR