Gauss-Manin

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Teichmuller Lift

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Relation to VHS attachments/Pasted%20image%2020220502184722.png

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Picard Lefschetz theory in Unsorted/Gauss-Manin
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.
Hodge F-crystal

See crystalline cohomology, Gauss-Manin, Hodge filtration, crystalline Frobenius.