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Answer by Harrison Brown for What does Faltings' theorem look like over...

I don't know enough arithmetic geometry to understand more than, like, half the words that I had to think about to find this reference, but if I'm understanding everything correctly, I think that...

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Answer by Pete L. Clark for What does Faltings' theorem look like over...

The "function field analogues" of Faltings' theorem were proved by Manin, Grauert and Samuel:...

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What does Faltings' theorem look like over function fields?

Minhyong Kim's reply to a question John Baez once asked about the analogy between $\text{Spec } \mathbb{Z}$ and 3-manifolds contains the following snippet:Finally, regarding the field with one element....

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