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SUMMARY:Pitchayut (Mark) Saengrungkongka (MIT)
DTSTART:20260305T220000Z
DTEND:20260305T233000Z
DTSTAMP:20260422T220048Z
UID:STAGE/151
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/151/">
 Examples of descent</a>\nby Pitchayut (Mark) Saengrungkongka (MIT) as part
  of STAGE\n\nLecture held in Room 2-139 in the MIT Simons Building.\n\nAbs
 tract\nThe main theorem of descent states that if $X$ is a smooth proper v
 ariety over global field $k$\, $G$ is a smooth affine algebraic group over
  $k$\, and $f : Z\\to X$ is a $G$-torsor over $X$\, then the $k$-rational 
 points of $X$ correspond to a union of $k$-rational points of finitely man
 y twists of $Z$. This reduces the problem of finding rational points of $X
 $ to finding rational points of finitely many twists of $Z$. We illustrate
  this theorem through several examples\, including the Weak Mordell-Weil T
 heorem.\n\nReference: Poonen\, <a href="https://math.mit.edu/~poonen/paper
 s/Qpoints.pdf"><i>Rational points on varieties</i></a>\, Section 8.3.\, 8.
 4.1-2\, 8.4.4-5.\n
LOCATION:https://researchseminars.org/talk/STAGE/151/
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