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SUMMARY:Bianca Viray (University of Washington)
DTSTART:20210928T203000Z
DTEND:20210928T213000Z
DTSTAMP:20260423T125049Z
UID:MITNT/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/32/">Q
 uadratic points on intersections of quadrics</a>\nby Bianca Viray (Univers
 ity of Washington) as part of MIT number theory seminar\n\nLecture held in
  Room 2-143 in the Simons building (building 2).\n\nAbstract\nA projective
  degree $d$ variety always has a point defined over a degree $d$ field ext
 ension.  For many degree $d$ varieties\, this is the best possible stateme
 nt\, that is\, there exist classes of degree $d$ varieties that never have
  points over extensions of degree less than $d$ (nor even over extensions 
 whose degree is nonzero modulo $d$).  However\, there are some classes of 
 degree $d$ varieties that obtain points over extensions of smaller degree\
 , for example\, degree $9$ surfaces in $\\mathbb{P}^9$\, and $6$-dimension
 al intersections of quadrics over local fields.  In this talk\, we explore
  this question for intersections of quadrics.  In particular\, we prove th
 at a smooth complete intersection of two quadrics of dimension at least $2
 $ over a number field has index dividing $2$\, i.e.\, that it possesses a 
 rational $0$-cycle of degree $2$.  This is joint work with Brendan Creutz.
 \n
LOCATION:https://researchseminars.org/talk/MITNT/32/
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