The Intrinsic Hodge Theory of p-adic Hyperbolic Curves by Shinichi Mochizuki §1. Introduction (A.) The Fuchsian Uniformization A hyperbolic curve is an algebraic curve obtained by removing r points from a smooth, proper

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• Algebraic geometry
• Number theory
• P-adic Teichmller theory
• P-adic number
• Riemann surface
• P-adic Hodge theory
• Nilcurve
• Differential geometry of surfaces
• Tate conjecture
• Algebraic curve
• Elliptic curve
• tale cohomology