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SUMMARY:Borys Kadets (Hebrew University)
DTSTART:20240402T203000Z
DTEND:20240402T213000Z
DTSTAMP:20260423T125736Z
UID:MITNT/90
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/90/">C
 urves with many degree $d$ points</a>\nby Borys Kadets (Hebrew University)
  as part of MIT number theory seminar\n\nLecture held in Room 2-449 in the
  Simons Building (building 2).\n\nAbstract\nWhen does a nice curve $X$ ove
 r a number field $k$ have infinitely many closed points of degree $d$?\nFa
 ltings' theorem allows us to rephrase this problem in purely algebro-geome
 tric terms\, though the resulting geometric question is far from being ful
 ly solved. Previous work gave easy to state answers to the problem for deg
 rees $2$ (Harris-Silverman) and $3$ (Abramovich-Harris)\, but also uncover
 ed exotic constructions of such curves in all degrees $d \\geqslant 4$ (De
 barre-Fahlaoui). I will describe recent progress on the problem\, which an
 swers the question in the large genus case. Along the way we uncover syste
 matic explanations for the Debarre-Fahlaoui counstructions and provide a c
 omplete geometric answer for $d \\leqslant 5$. The talk is based on joint 
 work with Isabel Vogt.\n
LOCATION:https://researchseminars.org/talk/MITNT/90/
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