In mathematics, a nilcurve is a pointed stable curve over a finite field with an indigenous bundle whose p-curvature is square nilpotent. Nilcurves were introduced by Mochizuki (1996) as a central concept in his theory of p-adic Teichmüller theory.
The nilcurves form a stack over the moduli stack of stable genus g curves with r marked points in characteristic p, of degree p.
References
- Mochizuki, Shinichi (1999), Foundations of p-adic Teichmüller theory, AMS/IP Studies in Advanced Mathematics, vol. 11, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1190-0, MR 1700772
- Mochizuki, Shinichi (1996), "A theory of ordinary p-adic curves", Kyoto University. Research Institute for Mathematical Sciences. Publications, 32 (6): 957–1152, doi:10.2977/prims/1195145686, hdl:2433/59800, ISSN 0034-5318, MR 1437328