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.
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