Arithmetic geometry arose as a beautiful and powerful theoryunifying geometry and number theory, formalizingstriking analogies between them in a way that allowedtools, results, and intuition of each to be transported tothe other—a notable example of this is the proof of thecenturies-old problem, Fermat’s Last Theorem. This theoryprovides a geometric viewpoint of objects over fields of prime characteristic ??, like finite fields. Decades after these ideas were formalized, characteristic ?? arithmetic geometry is rapidly expanding to include work in the vibrant young fields of arithmetic dynamics and derived algebraic geometry.
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