2015/05/18 by Yasuda, Takehiko
#11G50 #11R21 #11R45 #14E16 #14G05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1505.04555
By a heuristic argument, we relate two conjectures. One is a version of Manin's conjecture about the distribution of rational points on a Fano variety. We concern specific singular Fano varieties, namely quotients of projective spaces by finite group actions, and their singularities play a key role. The other conjecture is a generalization of Malle's conjecture about the distribution of extensions of a number field. Main tools are several Dirichlet series and previously obtained techniques, especially the untwisting, for the counterpart over a local field.