English

Rational points of universal curves

Number Theory 2011-04-13 v3 Algebraic Geometry

Abstract

In this paper we prove a version of Grothendieck's section conjecture for the restriction of the universal complete curve over M_{g,n}, g > 4, to the function field k(M_{g,n}) where k is, for example, a number field. In this version, the fundamental group of the closed fiber is replaced by its ell-adic unipotent completion when n > 1.

Keywords

Cite

@article{arxiv.1001.5008,
  title  = {Rational points of universal curves},
  author = {Richard Hain},
  journal= {arXiv preprint arXiv:1001.5008},
  year   = {2011}
}

Comments

60 pages. This is a minor revision of the previous version. To appear in JAMS

R2 v1 2026-06-21T14:40:19.742Z