Rational points of universal curves

Details Rational points of universal curves Rational points of universal curves

2010-01-27

arxiv.org/abs/1001.5008v3

J. Amer. Math. Soc. 24 (2011), 709-769

Mathematics

Number Theory

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

Scientific paper

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.

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