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Explore a comprehensive lecture on Shimurian analogs of Barsotti-Tate groups delivered by Vladimir Drinfeld from the University of Chicago. Begin with a review of Grothendieck's concept of n-truncated Barsotti-Tate groups and their formation of an algebraic stack over integers. Delve into the challenges of providing an illuminating description of reductions modulo powers of p and constructing analogs related to general Shimura varieties with good reduction at p. Examine conjectures addressing these problems, which have been proven by Z. Gardner, K. Madapusi, and A. Mathew, including their development of a modern version of Dieudonné theory. Gain insights into advanced mathematical concepts and their applications in this 1-hour 18-minute presentation from the Institut des Hautes Etudes Scientifiques (IHES).
