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Nilcurve
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 * *{{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 Algeb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indigenous Bundle
In mathematics, an indigenous bundle on a Riemann surface is a fiber bundle with a flat connection associated to some complex projective structure. Indigenous bundles were introduced by . Indigenous bundles for curves over p-adic fields were introduced by in his study 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 .... References * * Riemann surfaces {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 introduced and developed by . The first problem is to reformulate the Fuchsian uniformization of a complex Riemann surface (an isomorphism from the upper half plane to a universal covering space of the surface) in a way that makes sense for ''p''-adic curves. The existence of a Fuchsian uniformization is equivalent to the existence of a canonical indigenous bundle over the Riemann surface: the unique indigenous bundle that is invariant under complex conjugation and whose monodromy representation is quasi-Fuchsian. For ''p''-adic curves the analogue of complex conjugation is the Frobenius endomorphism, and the analogue of the quasi-Fuchsian condition is an integrality condition on the indigenous line bundle. So ''p''-adic Teichmüller theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |