Rational points of universal curves

Richard Hain

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arXiv · 1001.5008

Rational points of universal curves

Richard Hain

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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.

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Richard Hain. 2010-01-27. Rational points of universal curves. https://arxiv.org/abs/1001.5008

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