University of Cambridge > > Number Theory Seminar > Paucity of rational points on fibrations with multiple fibres

Paucity of rational points on fibrations with multiple fibres

Add to your list(s) Download to your calendar using vCal

  • UserJulian Lyczak (University of Bath)
  • ClockTuesday 21 November 2023, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Hanneke Wiersema.

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. Using exact conditions for a fibre to be locally soluble, coming from logarithmic geometry, we can translate the counting problem into a purely analytical question. Then using the large sieve we obtain upper bounds for the relevant counting problems for several families of examples. In some cases we can also provide lower bounds of the same order, and even asymptotics. Using these results I will discuss different ways in which the Loughran-Smeets conjecture depends on the absence of multiple fibres, and indicate the geometry involved in stating a conjecture for the general setting.

This talk is part of the Number Theory Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity