On rationally connected varieties over $C_1$ fields of characteristic $0$

Marta Pieropan

On rationally connected varieties over $C_1$ fields of characteristic $0$

Algebraic Geometry 2021-08-06 v2 Number Theory

Authors: Marta Pieropan

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 $C_1$ -conjecture. We also provide evidence that supports the conjecture in dimension $3$ for $C_1$ fields of characteristic $0$ .

Keywords

rationally connected varieties C1 fields characteristic 0 rational points terminal fano varieties birational geometry c1 conjecture

Cite

@article{arxiv.1905.02227,
  title  = {On rationally connected varieties over $C_1$ fields of characteristic $0$},
  author = {Marta Pieropan},
  journal= {arXiv preprint arXiv:1905.02227},
  year   = {2021}
}

Comments

30 pages; major revision, sections 4 and 5 added

On rationally connected varieties over $C_1$ fields of characteristic $0$

Abstract

Keywords

Cite

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