Generalizations of Ohta's Theorem for Holomorphic Modular Forms on Certain Shimura Varieties

Explore a mathematics lecture that delves into the generalization of Ohta's theorem for holomorphic modular forms on Shimura varieties, with particular emphasis on Hilbert modular varieties. Learn how Marco Sangiovanni and Chris Skinner extend Ohta's description of ordinary parts in étale cohomology of modular curve towers through Hida families, moving beyond the one-dimensional constraints of the original theorem. Discover how their approach incorporates Faltings' ideas, refined through Bhatt's framework of integral p-adic Hodge theory, and understand its potential applications in constructing Euler systems. Examine the theoretical foundations developed by Bhatt-Morrow-Scholze, Bhatt-Scholze, and Bhatt-Lurie that support this mathematical advancement in arithmetic geometry.