Peter Scholze
fl. 1987, Dresden, East Germany
Arithmetic and number theoryAlgebraGeometryFields Medal 2018
German mathematician who created perfectoid spaces and transformed modern arithmetic geometry.
Peter Scholze introduced perfectoid spaces, a framework that transports difficult questions between characteristic zero and positive characteristic. His work has influenced p-adic geometry, the Langlands program, and arithmetic geometry. He received the 2018 Fields Medal.
Workplaces: University of Bonn
Germany
Award-winning work
Fields Medal 2018The 2018 Fields Medal cited Scholze for transforming arithmetic algebraic geometry over p-adic fields through the introduction of perfectoid spaces. Perfectoid spaces allow Galois-theoretic and geometric problems in mixed characteristic to be tilted into characteristic p, where Frobenius makes them tractable, and then tilted back — resolving long-standing questions such as the weight-monodromy conjecture in many cases. Together with his new theories of étale and pro-étale cohomology for p-adic varieties, this framework produced striking applications, including local Langlands correspondences for new classes of groups and cohomology bounds for arithmetic manifolds. His work with Bhatt and others also reshaped integral p-adic Hodge theory.