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SUMMARY:Nonexistence of quadratic points on del Pezzo surfaces of d
 egree 4 over global function fields - Katerina Santicola (University of 
 Bath)
DTSTART:20251021T133000Z
DTEND:20251021T143000Z
UID:TALK238012@talks.cam.ac.uk
CONTACT:Bence Hevesi
DESCRIPTION:Colliot-Thélène recently asked whether every del Pezzo surfa
 ce of degree 4 (dP4) has a quadratic point over a $C_2$ field. This questi
 on has counterexamples over $C_3$ fields and a positive result over $C_1$ 
 fields but remained open for all $C_2$ fields. Last year Creutz and Viray 
 built an infinite family of dP4s without quadratic points over $\\mathbb{Q
 }$.  In work in progress\, we follow their method to construct an infinite
  family of dP4s with a Brauer-Manin obstruction to a quadratic point over 
 $\\mathbb{F}_p(t)$ for all $p\\neq 2$\, thus answering Colliot-Thélène's
  question in the negative. This is joint work with Giorgio Navone\, Harry 
 Shaw and Dr Haowen Zhang.\n
LOCATION:MR13
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