An overview of abelian varieties in homotopy theory

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This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the conference "New Topological Contexts for Galois Theory and Algebraic Geometry."
36 pages, minor corrections, repaired errors in final formulas

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