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Explore an advanced mathematics lecture from the University of Chicago Number Theory / Geometric Langlands Seminar where Jacob Lurie delves into the theory of prismatic cohomology and its applications. Learn about the groundbreaking work by Bhatt and Scholze in developing prismatic cohomology as a cohomology theory for p-adic formal schemes, and discover how it connects various arithmetic and geometric invariants. Understand the concept of prismatization of formal schemes and its relationship to coherent cohomology, with a particular focus on the theoretical prismatization of the field with one element (F₁). Examine how this mathematical construction provides insights into recent developments in syntomic cohomology theory.
