<p>For the moduli stack $\mathcal{M}_{g,n/\mathbb{F}_p}$ of smooth curves of type $(g,n)$ over Spec $\mathbb{F}_p$ with the function field $K$, we show that if $g\geq3$, then the only $K$-rational points of the generic curve over $K$ are its $n$ tautological points. Furthermore, we show that if $g\geq 3$ and $n=0$, then Grothendieck's Section Conjecture holds for the generic curve over $K$. A primary tool used in this thesis is the theory of weighted completion developed by Richard Hain and Makoto Matsumoto.</p> / Dissertation
| Identifer | oai:union.ndltd.org:DUKE/oai:dukespace.lib.duke.edu:10161/9874 |
| Date | January 2015 |
| Creators | Watanabe, Tatsunari |
| Contributors | Hain, Richard M |
| Source Sets | Duke University |
| Detected Language | English |
| Type | Dissertation |
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