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1.

### Perfectoid Spaces

| Springer Verlag | 2012

Abstract

We introduce a certain class of so-called perfectoid rings and spaces, which give a natural ...
2.

### Le lemme d’Abhyankar perfectoide

| Springer Verlag | 2017
perfectoïde du lemme d’Abhyankar du théorème de presque-pureté, par un passage à la limite mettant en jeu des versions perfectoïdes du théorème ...
3.

### Overconvergent Hilbert modular forms via perfectoid modular varieties

Freier Zugriff
| arXiv | 2019
perfectoid Hilbert modular varieties at infinite level. We show that our definition varies in $p$-adic weight families, and compare it to an earlier ...
4.

### Drinfeld's lemma for perfectoid spaces and overconvergence of multivariate $(\varphi, \Gamma)$-modules

Freier Zugriff
| arXiv | 2018
6.

### Perfectoid spaces and the homological conjectures

Freier Zugriff
| arXiv | 2018
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid ...
7.

### Singularities in mixed characteristic. The perfectoid approach

Freier Zugriff
| arXiv | 2018
theory, a powerful tool to investigate singularities in characteristic p. Recently, perfectoid techniques coming from p-adic Hodge theory have ...
8.

### Perfectoid Tate Curve

Freier Zugriff
| arXiv | 2018
Perfectoid versions of Abel Jacobi and Reimann Roch Theorem are proved, and perfectoid Elliptic Curve is constructed. A Perfectoid Tate ...
9.

### Integral perfectoid big Cohen–Macaulay algebras via André’s theorem

| Springer Verlag | 2018
characteristic maps to an integral perfectoid big Cohen–Macaulay algebra. The proof of this result is based on the construction of almost Cohen–Macaulay ...
10.

### Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers

| Springer Verlag | 2018

Abstract

Using perfectoid algebras we introduce a mixed characteristic analog of the multiplier ideal ...
11.

### Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras

Freier Zugriff
| arXiv | 2018
We utilize recent results of Andr\'e and Gabber on the existence of weakly functorial integral perfectoid big Cohen-Macaulay (BCM) algebras ...
12.

### Integral perfectoid big Cohen-Macaulay algebras via Andr\'e's theorem

Freier Zugriff
| arXiv | 2017
13.

### Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers

Freier Zugriff
| arXiv | 2017
Using perfectoid algebras, we introduce a mixed characteristic analog of the multiplier ideal, respectively test ideal, from characteristic ...
14.

### Geometry of Projective Perfectoid and Integer Partitions

Freier Zugriff
| arXiv | 2017
Line bundles of rational degree are defined using Perfectoid spaces, and their co-homology computed via standard \v{C}ech complex along ...
15.

### Overconvergent Modular Forms and Perfectoid Shimura Curves

| DataCite | 2017
16.

### Perfectoid Shimura Varieties of Abelian Type

| British Library Online Contents | 2017
17.

### Complex orientations for THH of some perfectoid fields

Freier Zugriff
| arXiv | 2016
perfectoid fields; and that the resulting spectra provide geometrically interesting targets for analogs of the Chern character, defined for certain ...
18.

### Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations II: wild case

Freier Zugriff
| arXiv | 2016
We construct a family of affinoids in the Lubin-Tate perfectoid space and their formal models such that the middle cohomology of their ...
19.

### Dieudonn\'e theory over semiperfect rings and perfectoid rings

Freier Zugriff
| arXiv | 2016
commutative finite locally free p-group schemes over perfectoid rings by Breuil-Kisin-Fargues modules if p>2. ...
20.

### Perfectoid Shimura Varieties of Abelian Type

| Online Contents | 2016

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