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SUMMARY:Paucity of rational points on fibrations with multiple fibres - Ju
 lian Lyczak (University of Bath)
DTSTART:20231121T143000Z
DTEND:20231121T153000Z
UID:TALK206776@talks.cam.ac.uk
CONTACT:Hanneke Wiersema
DESCRIPTION:This talk is based on joint work with Browning and Smeets and 
 concerns the density of everywhere locally soluble members within a family
  of varieties. Our work treats the most general case\, where components of
  higher multiplicity are allowed.\nUsing exact conditions for a fibre to b
 e locally soluble\, coming from logarithmic geometry\, we can translate th
 e counting problem into a purely analytical question. Then using the large
  sieve we obtain upper bounds for the relevant counting problems for sever
 al families of examples. In some cases we can also provide lower bounds of
  the same order\, and even asymptotics.\nUsing these results I will discus
 s different ways in which the Loughran-Smeets conjecture depends on the ab
 sence of multiple fibres\, and indicate the geometry involved in stating a
  conjecture for the general setting.
LOCATION:MR13
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