Rational points of universal curves
Abstract
In this paper we prove a version of Grothendieck's section conjecture for the restriction of the universal complete curve over Mg,n, g > 4, to the function field k(Mg,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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