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Hodge index theorem
Proof: Riemann-Roch for surfaces.
Corollaries
Hodge index theorem
- weak and hard Lefschetz theorems
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arithmetic intersection theory
Manin proves the Mordell conjecture using the Gauss-Manin connection, generalized to Areklov theory. Uses Green functions on curves. Used in Faltings theorem. Imports tools like the adjunction formula, the Hodge index theorem, Riemann-Roch.
- Kahler