On rationally connected varieties over C₁ fields of characteristic 0

2019/05/06 by Pieropan, Marta
#14G05 #14J45 (secondary) #14M22 (primary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.02227

Abstract

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequences of this result, especially in relation to the C₁-conjecture. We also provide evidence that supports the conjecture in dimension 3 for C₁ fields of characteristic 0.

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