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On Picard groups of perfectoid covers of toric varieties
Springer Verlag | 2023|Let X be a proper smooth toric variety over a perfectoid field of prime residue
...Schlagwörter: Perfectoid spaces -
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 $\mathrm{K}$-Theory of Perfectoid Rings
Freier ZugriffDataCite | 2022|We establish various properties of the $p$-adic algebraic $\mathrm{K}$-theory of smooth algebras over perfectoid rings living over ... -
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 Spaces: An Annotated Bibliography
Springer Verlag | 2022|This annotated bibliography was prepared as part of a five-lecture series at the summer school on perfectoid
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The Relative (de-)Perfectoidification Functor and Motivic p-Adic Cohomologies
Springer Verlag | 2022|p-adic realizations, and we show that rigid analytic and perfectoid motives are equivalent over a base of characteristic p. ... -
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 ... -
Perfectoid Spaces
TIBKAT | 2022|On ψ-Lattices in Modular (φ, Γ)-Modules -- The Relative (De-)Perfectoidification Functor and Motivic P-Adic Cohomologies -- Diagrams 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 ... -
Projective geometry for perfectoid spaces
Freier ZugriffBASE | 2021|We develop a perfectoid analog of projective geometry and explore how equipping a perfectoid space with a map to a certain analog of ... -
$p$-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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