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Geometric and arithmetic theta correspondences (2402.12159v2)
Published 19 Feb 2024 in math.NT, math.AG, and math.RT
Abstract: Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. We give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also known as the Kudla program) and their applications. These are expanded lecture notes for the IHES 2022 Summer School on the Langlands Program.
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