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Explore advanced arithmetic geometry concepts in this hour-long lecture examining the obstruction to lifting Frobenius on Shimura varieties and its applications to companion forms theory. Delve into the geometric framework for understanding companion forms in both classical modular forms contexts, building on foundational work by Gross, Coleman-Voloch, and Faltings-Jordan, and extend these concepts to higher-dimensional cases. Learn how Frobenius lifting techniques provide new insights into the structure of modular forms and their geometric interpretations through Shimura varieties. Discover the mathematical connections between algebraic geometry, number theory, and modular forms as the speaker presents cutting-edge research in arithmetic geometry. Gain understanding of how geometric methods can illuminate classical problems in the theory of automorphic forms and their p-adic properties.
