20/05/04 16:32:33 ncpDqOGk.net
>>22 補足
落合 理先生 2009年のサマースクール
一方、ショルツ先生の”Perfectoid space”登場が、2012年ころというから
Perfectoidの直前の話ですね
URLﾘﾝｸ(en.wikipedia.org)
Perfectoid space
In mathematics, perfectoid spaces are adic spaces of special kind, which occur in the study of problems of "mixed characteristic", such as local fields of characteristic zero which have residue fields of characteristic prime p.
A perfectoid field is a complete topological field K whose topology is induced by a nondiscrete valuation of rank 1, such that the Frobenius endomorphism Φ is surjective on K°/p where K° denotes the ring of power-bounded elements.
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]
Contents
1 Tilting equivalence
1.1 Almost purity theorem