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Unirationality of conic bundles over finite fields

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  • UserElyes Boughattas (University of Rennes 1)
  • ClockTuesday 18 November 2025, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Bence Hevesi .

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, Yanchevskiĭ asked whether a surface X is unirational when f:X->P1 is a conic bundle. In 1996, Mestre had supplied a positive answer when the cardinal 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 P1 . As a bonus, and under the same conditions, the method we use proves that X has a unique R-equivalence class. (arXiv:2410.19686v2)

This talk is part of the Number Theory Seminar series.

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