Rapoport, Michael The work of Peter Scholze. (English) Zbl 1441.11002 Sirakov, Boyan (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2018, Rio de Janeiro, Brazil, August 1–9, 2018. Volume I. Plenary lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 71-85 (2018). Summary: Peter Scholze has developed powerful methods in algebraic geometry over \(p\)-adic fields, and has proved striking theorems in this area.For the entire collection see [Zbl 1436.00059]. Cited in 1 Document MSC: 11-02 Research exposition (monographs, survey articles) pertaining to number theory 11-03 History of number theory 14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry 14-03 History of algebraic geometry 14G45 Perfectoid spaces and mixed characteristic 11F77 Automorphic forms and their relations with perfectoid spaces 14G22 Rigid analytic geometry 01A61 History of mathematics in the 21st century 11S37 Langlands-Weil conjectures, nonabelian class field theory 11R39 Langlands-Weil conjectures, nonabelian class field theory 11F80 Galois representations 01A70 Biographies, obituaries, personalia, bibliographies Keywords:perfectoid spaces; pro-étale topology; cohomology theories; Shimura varieties Biographic References: Scholze, Peter PDFBibTeX XMLCite \textit{M. Rapoport}, in: Proceedings of the international congress of mathematicians 2018, ICM 2018, Rio de Janeiro, Brazil, August 1--9, 2018. Volume I. Plenary lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 71--85 (2018; Zbl 1441.11002) Full Text: DOI arXiv