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SUMMARY:Xinyu Fang (Harvard)
DTSTART:20260416T210000Z
DTEND:20260416T223000Z
DTSTAMP:20260422T220630Z
UID:STAGE/156
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/156/">
 Descent varieties and Brauer-Manin obstruction on diagonal cubic surfaces<
 /a>\nby Xinyu Fang (Harvard) as part of STAGE\n\nLecture held in Room 2-13
 9 in the MIT Simons Building.\n\nAbstract\nDiagonal cubic surfaces are an 
 interesting class of varieties in the context of the Hasse principle\, sin
 ce they have a very simple form and the Brauer-Manin obstruction is conjec
 tured to be the only obstruction to the Hasse principle.\n\nIn this talk\,
  we construct torsors over diagonal cubic surfaces under a torus\, which p
 lay the role of the universal torsor. We define the "type" of a torsor\, a
 nd the obstruction defined by a given type. The main theorem is the equiva
 lence between the Brauer-Manin obstruction and the obstruction defined by 
 torsors of type $i$ that we constructed earlier. This reduces the problem 
 of whether "the Brauer-Manin obstruction is the only one" to the validity 
 of the Hasse principle for these torsors.\n\nReference: \n\n1. Colliot-Th
 élène\, Kanevsky\, and Sansuc\, <a href="https://link.springer.com/chapt
 er/10.1007/BFb0078705">Arithmétique des surfaces cubiques diagonales</a>\
 , Section 10(c) + Proposition 10 from (d).\n(<a href="https://drive.google
 .com/file/d/1okKy8o68IfdmgiOnRCAxYKE4D46yEdZa/view?usp=sharing">English tr
 anslation</a>)\n\n2. Colliot-Thélène and Sansuc. La descente sur les var
 iétés rationnelles\, II. (1987)\n
LOCATION:https://researchseminars.org/talk/STAGE/156/
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