- In mathematics,
perfectoid spaces are adic
spaces of
special kind,
which occur in the
study of
problems of "mixed characteristic", such as
local fields...
- Faltings, Jean-Marc
Fontaine and
later by
Kiran Kedlaya. His PhD
thesis on
perfectoid spaces yields the
solution to a
special case of the weight-monodromy conjecture...
- and by
Jonathan Pila in 2009. In 2016, André used Scholze's
method of
perfectoid spaces to
prove Melvin Hochster's
direct summand conjecture that any finite...
- Kiran; Scholze, Peter; Weinstein,
Jared (2019). Cais,
Bryden (ed.).
Perfectoid Spaces.
Mathematical Surveys and Monographs. Vol. 242. Providence, Rhode...
-
geometry of
certain Shimura varieties. In the 2010s,
Peter Scholze developed perfectoid spaces and new
cohomology theories in
arithmetic geometry over p-adic...
- an R-module. The
conjecture was
proven by Yves André
using a
theory of
perfectoid spaces. The
Canonical Element Conjecture. Let x 1 , … , x d {\displaystyle...
-
after the
first book, and
especially an
extended theory of
perfectoid rings and
perfectoid spaces which generalizes the
recent work of
Peter Scholze....
- t (in Fp((t))),
yields (infinite)
extensions of
these fields known as
perfectoid fields. Strikingly, the
Galois groups of
these two
fields are isomorphic...
-
Metric space Minkowski space Müntz
space Normed space Paracompact space Perfectoid space Planar space Polish space Probability space Projective space Proximity...
- from
interacting particle systems"
Peter Scholze "for his
invention of
perfectoid spaces and
their application to
fundamental problems in
algebraic geometry...
