Scientists / Open questions
Peter Scholze
Arithmetic geometry; p-adic geometry
2018 Fields Medal
4 questions
The unconditional Langlands-Kottwitz description of the cohomology of compact PEL Shimura varieties of type A at ramified split places at full -level: general stable character identities for pseudo-stabilized test functions, the stable Bernstein center, the monodromy operator, and Hecke isolation of local -packet representations
The weight-monodromy conjecture for proper smooth varieties over mixed-characteristic local fields
Poincaré duality, non-lisse direct images, and the non-proper extension in p-adic Hodge theory for rigid-analytic varieties
Drinfeld's question on a natural map between the -Čech complex and the de Rham-Witt complex (Bhatt-Morrow-Scholze, Question 8.16)