Displaying similar documents to “Existence of rational points on smooth projective varieties”

Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

Andrey Trepalin (2014)

Open Mathematics

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Let 𝕜 be a field of characteristic zero and G be a finite group of automorphisms of projective plane over 𝕜 . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field 𝕜 is algebraically closed. In this paper we prove that 𝕜 2 𝕜 2 G G is rational for an arbitrary field 𝕜 of characteristic zero.

A family of varieties with exactly one pointless rational fiber

Bianca Viray (2010)

Journal de Théorie des Nombres de Bordeaux

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We construct a concrete example of a 1 -parameter family of smooth projective geometrically integral varieties over an open subscheme of 1 such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.