Rational points of universal curves

2010/01/31 by Richard Hain · 4 citations
Mathematics · #math.AG #math.NT

paper · pdf

published as J. Amer. Math. Soc. 24 (2011), 709-769 · 60 pages. This is a minor revision of the previous version. To appear in JAMS

arxiv created 2010/12/30 · arxiv updated 2011/04/13

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.

Cited by

• Remarks on Non-Abelian Cohomology of Proalgebraic Groups
• Monodromy of Codimension-One Sub-Families of Universal Curves
• Rational points of universal curves in positive characteristics
• On the sections of universal hyperelliptic curves

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