arithmetic geometry

Equidistribution and the torsor method

arXiv:2607.14866

summary

The authors prove equidistribution and Manin's conjecture for rational points outside the lines on smooth split quintic del Pezzo surfaces over number fields, using a general torsor method applicable to multiple equivalent height functions.

Abstract

We prove equidistribution and Manin's conjecture for rational points outside the lines on smooth split quintic del Pezzo surfaces over number fields with respect to any anticanonical height. The proof is based on a general theorem that is broadly usable to deduce equidistribution when using the torsor method with several equivalent height functions to treat variants of Manin's problem.

23 pages, 1 figure

Topics & keywords

#rational points#del pezzo surfaces#manin's conjecture#equidistribution#torsor method#height functionssmooth split quintic del Pezzo surfaceanticanonical heighttorsorManin's conjecturenumber fields
Equidistribution and the torsor method · wovepaper