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 as a central concept in his theory of
p-adic Teichmüller theory
In mathematics, ''p''-adic Teichmüller theory describes the "uniformization" of ''p''-adic curves and their moduli, generalizing the usual Teichmüller theory that describes the uniformization of Riemann surfaces and their moduli. It was intr ...
.
The nilcurves form a stack over the moduli stack of stable genus ''g'' curves with ''r'' marked points in characteristic ''p'', of degree
''p''
3''g''–3+''r''.
References
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*{{Citation , last1=Mochizuki , first1=Shinichi , title=A theory of ordinary p-adic curves , doi=10.2977/prims/1195145686 , mr=1437328 , year=1996 , journal=Kyoto University. Research Institute for Mathematical Sciences. Publications , issn=0034-5318 , volume=32 , issue=6 , pages=957–1152, doi-access=free
Algebraic geometry