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Peter Scholze (German pronunciation: [ˈpeːtɐ ˈʃɔltsə] ⓘ; born 11 December 1987 [2]) is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn since 2012 and director at the Max Planck Institute for Mathematics since 2018.
Condensed mathematics is a theory developed by Dustin Clausen and Peter Scholze which replaces a topological space by a certain sheaf of sets, in order to solve some technical problems of doing homological algebra on topological groups.
Dustin Clausen is an American-Canadian [1] mathematician known for his contributions to algebraic K-theory and the development of condensed mathematics, in collaboration with Peter Scholze. His research interests include the intersections of number theory and homotopy theory .
The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians. [ 2 ] [ 3 ] [ 4 ] As of 1 December 2023, [update] it contained information on 300,152 mathematical scientists who contributed to research-level mathematics.
A simpler proof was suggested almost at the same time by Guy Henniart, [12] and ten years later by Peter Scholze. Taylor, together with Christophe Breuil , Brian Conrad and Fred Diamond , completed the proof of the Taniyama–Shimura conjecture , by performing quite heavy technical computations in the case of additive reduction.
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Perfectoid spaces may be used to (and were invented in order to) compare mixed characteristic situations with purely finite characteristic ones. Technical tools for making this precise are the tilting equivalence and the almost purity theorem. The notions were introduced in 2012 by Peter Scholze. [1]
In mathematics, especially in topology, a pyknotic set is a sheaf of sets on the site of compact Hausdorff spaces (with some fixed Grothendieck universes). The notion was introduced by Barwick and Haine to provide a convenient setting for homological algebra. [1] The term pyknotic comes from the Greek πυκνός, meaning dense, compact or ...