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Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers
Freier ZugriffArXiv | 2017|Using perfectoid algebras, we introduce a mixed characteristic analog of the multiplier ideal, respectively test ideal, from characteristic ... -
Formalising perfectoid spaces
Freier ZugriffArXiv | 2019|Perfectoid spaces are sophisticated objects in arithmetic geometry introduced by Peter Scholze in 2012. We formalised enough definitions ... -
Descent for solid quasi-coherent sheaves on perfectoid spaces
Freier ZugriffArXiv | 2024|We prove $v$-descent for solid quasi-coherent sheaves on perfectoid spaces as a key technical input for the development of a $6$-functor ... -
Real Topological Hochschild Homology of Perfectoid Rings
Freier ZugriffArXiv | 2023|We refine several results of Bhatt-Morrow-Scholze on THH to THR. In particular, we compute THR of perfectoid rings. This will be useful for ... -
Tilting and untilting for ideals in perfectoid rings
Freier ZugriffArXiv | 2023|For an (integral) perfectoid ring $R$ of characteristic $0$ with tilt $R^{\flat}$, we introduce and study a tilting map $(-)^{\flat}$ from ... -
A calculation of the perfectoidization of semiperfectoid rings
Freier ZugriffArXiv | 2023|We show that perfectoidization can be (almost) calculated by using $p$-root closure in certain cases, including the semiperfectoid case. To ... -
A Berkovich Approach to Perfectoid Spaces
Freier ZugriffArXiv | 2023|Since their inception perfectoid spaces have catalyzed a revolution in p-adic geometry. We redevelop the foundations of perfectoid spaces ... -
The perfectoid Tate algebra has uncountable Krull dimension
Freier ZugriffArXiv | 2022|Let $K$ be a perfectoid field with pseudo-uniformizer $\pi$. We adapt an argument of Du to show that the perfectoid Tate algebra $K\langle ... -
Perfectoid Nullstellensatz: Results and counterexamples
Freier ZugriffArXiv | 2022|Abstract. We give necessary conditions and we give sufficient conditions for perfectoid Nullstellensatz to hold. As a consequence, we prove ... -
A criterion for perfectoid fields
Freier ZugriffArXiv | 2022|The tilting correspondence is a fundamental property of perfectoid fields. In this note, we show that the tilting construction can also be ... -
Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundamental groups
Freier ZugriffArXiv | 2022|We define a (perfectoid) mixed characteristic version of $F$-signature and Hilbert-Kunz multiplicity by utilizing the perfectoidization ... -
$G$-torsors on perfectoid spaces
Freier ZugriffArXiv | 2022|$ in the $v$-topology. Our main result is that on perfectoid spaces, $G$-torsors in the \'etale and $v$-topology are equivalent. This ... -
$\mathrm{RO}(\mathbb T)$-graded $\mathrm{TF}$ of perfectoid rings
Freier ZugriffArXiv | 2022|For a perfectoid ring $R$, we compute the full $\mathrm{RO}(\mathbb T)$-graded ring $\mathrm{TF}_\bigstar(R;\mathbf Z_p)$. This extends and ... -
$K$-Theory of Cuspidal Curves Over a Perfectoid Base And Formal Analogues
Freier ZugriffArXiv | 2022|$ to the mixed characteristic setting using perfectoid rings. We extend the work of Hesselholt-Nikolaus in \cite{Hesselholt_Nikolaus} on the ... -
Perfectoid towers and their tilts : with an application to the \'etale cohomology groups of local log-regular rings
Freier ZugriffArXiv | 2022|To initiate a systematic study on the applications of perfectoid method to Noetherian rings, we introduce the notions of perfectoid towers ... -
The K-theory of perfectoid rings
Freier ZugriffArXiv | 2022|We establish various properties of the p-adic algebraic K-theory of smooth algebras over perfectoid rings living over perfectoid valuation ... -
The perfectoid commutant of Lubin-Tate power series
Freier ZugriffArXiv | 2022|power series that commutes with the elements of Aut(LT) is itself in Aut(LT). We extend this result to perfectoid power series, by lifting such ... -
Decompletion of cyclotomic perfectoid fields in positive characteristic
Freier ZugriffArXiv | 2022| -
Untilting Line Bundles on Perfectoid Spaces
Freier ZugriffArXiv | 2021|Let $X$ be a perfectoid space with tilt $X^\flat$. We construct a canonical map $\theta:\operatorname{Pic} X^\flat\to\lim\operatorname{Pic ... -
$p$-complete arc-descent for perfect complexes over integral perfectoid rings
Freier ZugriffArXiv | 2021|We prove $p$-complete arc-descent results for finite projective modules and perfect complexes over integral perfectoid rings. Using our ...
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