2018 Fields Medal (3)
Reason for Award
For transformingarithmetic algebraic geometryoverp-adic fieldsthrough his introduction ofperfectoid spaces, with application toGalois representations, and for the development of newcohomology theories.
Laureates
Peter Scholze,
Germany
Other works in the same year
- For the proof of the boundedness ofFano varietiesand for contributions to theminimal model program.
- For contributions to the theory ofoptimal transportand its applications inpartial differential equations,metric geometryandprobability.
- For his synthesis ofanalytic number theory, homogeneous dynamics,topology, andrepresentation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects.