English

Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons

Algebraic Geometry 2019-10-17 v2

Abstract

For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. In particular, the zero loci of those functions are algebraic and defined over such a field of definition. This proves a conjecture of Charles.

Keywords

Cite

@article{arxiv.1810.07404,
  title  = {Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons},
  author = {Jeff Achter and Sebastian Casalaina-Martin and Charles Vial},
  journal= {arXiv preprint arXiv:1810.07404},
  year   = {2019}
}

Comments

New title. 15 pages

R2 v1 2026-06-23T04:42:46.940Z