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SUMMARY:Rafael von Känel (IAS\, Tsinghua University)
DTSTART:20231121T210000Z
DTEND:20231121T220000Z
DTSTAMP:20260423T130231Z
UID:MITNT/81
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/81/">I
 ntegral points on the Clebsch-Klein surfaces</a>\nby Rafael von Känel (IA
 S\, Tsinghua University) as part of MIT number theory seminar\n\nLecture h
 eld in Room 2-449 in the Simons Building (building 2).\n\nAbstract\nIn thi
 s talk we present explicit bounds for the Weil height and the number of in
 tegral points on classical surfaces first studied by Clebsch (1871) and Kl
 ein (1873). Building on Hirzebruch’s work in which he related these surf
 aces to a Hilbert modular surface\, we deduced our bounds from a general r
 esult for integral points on coarse Hilbert moduli schemes. After explaini
 ng this deduction\, we discuss the strategy of proof of the general result
  which combines the method of Faltings (Arakelov\,\nParsin\, Szpiro) with 
 modularity\, Masser-Wuestholz isogeny estimates\, and results based on eff
 ective analytic estimates and/or Arakelov theory. Joint work with Arno Kre
 t.\n
LOCATION:https://researchseminars.org/talk/MITNT/81/
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