Rational points of universal curves in positive characteristics

2014/10/11 by Tatsunari Watanabe, Watanabe, Tatsunari
Arts and Humanities · Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #Historical Studies and Socio-cultural Analysis #Vietnamese History and Culture Studies #math.AG

paper · pdf · doi:10.48550/arxiv.1410.3020

31 pages. Significantly shortened. Proposition 4.3 from the 1st version had a mistake and is replaced with a weaker proposition. This article draws heavily from arXiv:1001.5008 "Rational points of universal curve." by Richard Hain and is an extension from char. zero to positive characteristic

arxiv created 2016/01/22 · arxiv updated 2016/01/25

Abstract

For the moduli stack M_g,n/\mathbbF_p of smooth curves over Spec~\mathbbF_p with the function field K, we show that if g≥3, then the only K-rational points of the generic curve over K are its n tautological points. Furthermore, we show that if g≥4 and n=0, then Grothendieck's Section Conjecture holds for the generic curve over K. This is an extension of Hain's work in characteristic 0 to positive characteristics.

Citations

• Rational points of universal curves

Related

• Rational points of universal curves
• The strong Franchetta Conjecture in arbitrary characteristics
• Curves with prescribed rational points
• Lower bounds on the maximal number of rational points on curves over finite fields
• Rational configuration problems and a family of curves