Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Rational points of universal curves in positive characteristics
HTML articles powered by AMS MathViewer

by Tatsunari Watanabe PDF
Trans. Amer. Math. Soc. 372 (2019), 7639-7676 Request permission

Abstract:

Let $K$ be the function field of the moduli stack ${\mathcal M}_{g,n/{\mathbb F}_p}$ of curves over $\text {Spec}{\mathbb F}_p$, and let $C/K$ be the restriction of the universal curve to $\text {Spec} K$. We show that if $g\geq 3$, then the only $K$-rational points of $C$ are its $n$ tautological points. Furthermore, we show that if $g\geq 4$ and $n=0$, then Grothendieck’s section conjecture holds for $C$ over $K$. This extends Hain’s work in characteristic $0$ to positive characteristics.
References
Similar Articles
Additional Information
  • Tatsunari Watanabe
  • Affiliation: Mathematics Department, Embry-Riddle Aeronautical University, Prescott, Arizona 86301
  • MR Author ID: 1256428
  • Email: watanabt@erau.edu
  • Received by editor(s): November 30, 2016
  • Received by editor(s) in revised form: January 4, 2019
  • Published electronically: July 29, 2019
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7639-7676
  • MSC (2010): Primary 14D23, 14D10, 14H30, 14H10
  • DOI: https://doi.org/10.1090/tran/7842
  • MathSciNet review: 4029677