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SUMMARY:Unirationality of conic bundles over finite fields - Elyes Boughat
 tas (University of Rennes 1)
DTSTART:20251118T143000Z
DTEND:20251118T153000Z
UID:TALK238018@talks.cam.ac.uk
CONTACT:Bence Hevesi
DESCRIPTION:Many results and conjectures in arithmetic geometry deal with 
 the existence and abundance of rational points on unirational varieties\, 
 that is\, those dominated by a projective space. Over a finite field\, Yan
 chevskiĭ asked whether a surface X is unirational when f:X->P^1^  is a co
 nic bundle. In 1996\, Mestre had supplied a positive answer when the cardi
 nal of the field is much larger than the degree of the "bad locus" of f. I
  will present a recent result where I answer Yanchevskiĭ's question when 
 the "bad fibres" of f lie above rational points of P^1^ . As a bonus\, and
  under the same conditions\, the method we use proves that X has a unique 
 R-equivalence class. (arXiv:2410.19686v2)\n\n
LOCATION:MR13
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