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Recently I asked Faltings for some references for a self-study of Arakelov theory beyond Lang’s Arakelov theory.

He suggested the following (all revolving around the arithmetic Riemann-Roch theorem):

1. Papers by Gillet and Soule on arithmetic intersection theory

2. Papers by Bismut, Gillet and Soule on determinant of cohomology of an arithmetic variety (towards Riemann-Roch for this determinant.)

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