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math.NT2018
The size of the primes obstructing the existence of rational points
Efthymios Sofos
The sequence of the primes for which a variety over has no -adic point plays a fundamental role in arithmetic geometry. This sequence is deterministic, however,…
math.NT2018
The density of fibres with a rational point for a fibration over hypersurfaces of low degree
Efthymios Sofos, Erik Visse
We prove asymptotics for the proportion of fibres with a rational point in a conic bundle fibration. The basis of the fibration is a general hypersurface of low degree.
math.NT2018
Rational points and prime values of polynomials in moderately many variables
Kevin Destagnol, Efthymios Sofos
We derive the Hasse principle and weak approximation for pencils of certain varieties in the spirit of work by Colliot-Thélène,Sansuc and Harpaz-Skorobogatov-Wittenberg. Our variet…