Special Year Workshop on p-adic Arithmetic Geometry

Explore advanced topics in p-adic arithmetic geometry through this comprehensive workshop featuring 15 specialized lectures from leading mathematicians at the Institute for Advanced Study. Delve into cutting-edge research areas including motivic cohomology of schemes, p-adic non-abelian Hodge theory, singularities in mixed characteristic, Igusa stacks and local-global compatibility, and K-theory of Z/p^n. Examine characteristic classes of étale local systems, prismatic crystals and q-Higgs modules, p-adic analytic geometry's connections to chromatic homotopy theory, and analytic prismatization techniques. Investigate Kirillov models for completed cohomology, duality theorems for p-adic pro-étale cohomology of Stein spaces, and vanishing results for rational completed cohomology of Shimura varieties. Study the analytic topology for B_dR^+-Grassmannians, categorification and geometry, and multiplicative polynomial laws with commutative group schemes. Gain insights from expert presentations by Matthew Morrow, Ben Heuer, Karl Schwede, Mingjia Zhang, Achim Krause, Alexander Petrov, Takeshi Tsuji, Tomer Schlank, Peter Scholze, Pierre Colmez, Wieslawa Niziol, Lue Pan, Kęstutis Česnavičius, Lars Hesselholt, and Akhil Mathew, covering the most current developments in this specialized field of algebraic geometry and number theory.