English

The split torsor method for Manin's conjecture

Number Theory 2020-05-06 v2 Algebraic Geometry

Abstract

We introduce the split torsor method to count rational points of bounded height on Fano varieties. As an application, we prove Manin's conjecture for all nonsplit quartic del Pezzo surfaces of type A3+A1\mathbf A_3+\mathbf A_1 over arbitrary number fields. The counting problem on the split torsor is solved in the framework of o-minimal structures.

Keywords

Cite

@article{arxiv.1907.09431,
  title  = {The split torsor method for Manin's conjecture},
  author = {Ulrich Derenthal and Marta Pieropan},
  journal= {arXiv preprint arXiv:1907.09431},
  year   = {2020}
}

Comments

36 pages; minor revision

R2 v1 2026-06-23T10:27:22.632Z