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Rational points over C1-fields of characteristic 0

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Pieropan, Marta

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Rational points over C1-fields of characteristic 0
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23
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You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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In the 1950s Lang studied the properties of C1 fields, that is, fields over which every hypersurface of degree at most n in a projective space of dimension n has a rational point. Later he conjectured that every smooth proper rationally connected variety over a C1 field has a rational point. I will explain how to find rational points on rationally connected threefolds over C1 fields of characteristic 0.