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Arithmetic geometry is at the interface between algebraic geometry and number theory, and studies schemes over the ring of integers of number fields, or their -adic completions, and connects with representation theory, automorphic forms, Hodge theory, algebraic topology, and many other fields.
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Gerd Faltings, Johan de Jong, Peter Scholze, Arithmetic Geometry. Oberwolfach Rep. 17 (2020), no. 2, pp. 1023–1082DOI 10.4171/OWR/2020/20