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on the Arakelov theory of arithmetic
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https://www.youtube.com/watch?v=v7juozS6AdE&list=PLx5f8IelFRgHmtrqss-4c4r9fMtPB2fps Let X be a semi-stable arithmetic surface of genus at least two and $\omega$ the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bail
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