Quantitative Ell-Adic Sheaf Theory

Explore a comprehensive lecture on quantitative ell-adic sheaf theory presented by Will Sawin from Columbia University at the AGNES 2023 conference held at Stony Brook University. Delve into the powerful tool of sheaf cohomology in algebraic geometry and its applications to other fields. Examine Katz's bounds for the dimension of étale cohomology groups and discover how these bounds can be extended to be compatible with the six functors formalism. Learn about joint work with Arthur Forey, Javier Fresán, and Emmanuel Kowalski, which introduces the concept of sheaf "complexity" and controls its growth under various operations. Understand the utility of étale cohomology groups and their dimensional bounds in concrete situations through a pre-talk explanation. Gain insights into this advanced topic in algebraic geometry over the course of 1 hour and 3 minutes.