Categorical Local Langlands for GL_n - The Irreducible Case with Integral Coefficients

Explore the categorical local Langlands correspondence for GL_n in this advanced mathematics lecture, focusing on the irreducible case with integral coefficients. Delve into the Fargues-Scholze conjecture, which proposes a Hecke-equivariant equivalence of categories between certain coherent sheaves on the stack of Langlands parameters and compact objects in the category of lisse-etale sheaves on Bun_G. Examine the proof of this conjecture for irreducible parameters for GL_n, even with integral coefficients, and discover how it requires surprisingly little knowledge about the spaces involved. Investigate the non-formal input, including the cardinality of the Fargues-Scholze L-packets and genericity of their members, as well as the formal input concerning localizations of categories over schemes. Gain insights into this complex mathematical topic through Konrad Zou's comprehensive presentation at the Hausdorff Center for Mathematics.