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SUMMARY:Yutong Chen (MIT)
DTSTART:20260312T210000Z
DTEND:20260312T223000Z
DTSTAMP:20260422T220125Z
UID:STAGE/152
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/152/">
 The descent obstruction</a>\nby Yutong Chen (MIT) as part of STAGE\n\nLect
 ure held in Room 2-139 in the MIT Simons Building.\n\nAbstract\nIn this ta
 lk\, we will briefly review the notion of Selmer sets and how they provide
  an obstruction to the existence of rational points. We will then prove a 
 theorem showing that\, the Selmer set is finite in interested cases. Next\
 , we will define the descent obstruction to the local-global principle and
  compare it with the Brauer-Manin obstruction. Finally\, we will construct
  explicit torsors over Iskovskikh's surface to demonstrate that it exhibit
 s a descent obstruction and\, in particular\, possesses no rational points
 . We may also apply descent obstruction to see the failure of strong appro
 ximation if time permits.\n\nReference: Poonen\, <a href="https://math.mit
 .edu/~poonen/papers/Qpoints.pdf"><i>Rational points on varieties</i></a>\,
  Section 8.1\,8.4\, 8.5.1.\n
LOCATION:https://researchseminars.org/talk/STAGE/152/
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