Christian Klevdal

activity

20202026

collaborators

6 papers

math.NT2026

Admissible pairs and $p$ -adic Hodge structures III: Variation and unlikely intersection

Sean Howe, Christian Klevdal

We extend the relative theory of admissible pairs and $p$ -adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $Q_{p}$ -vector sp…

math.NT2025

Compatibility of $F$ -isocrystals on adjoint Shimura varieties

Jake Huryn, Kiran S. Kedlaya, Christian Klevdal +1

In this article, we extend past results of the last two authors to include compatibility of canonical $ℓ$ -adic local systems and canonical $F$ -isocrystals on adjoint Shimura var…

math.NT2023

Admissible pairs and $p$ -adic Hodge structures I: Transcendence of the de Rham lattice

Sean Howe, Christian Klevdal

For an algebraically closed non-archimedean extension $C / Q_{p}$ , we define a Tannakian category of $p$ -adic Hodge structures over $C$ that is a local, $p$ -adic analog of the…

math.NT2023

Admissible pairs and $p$ -adic Hodge structures II: The bi-analytic Ax-Lindemann theorem

Sean Howe, Christian Klevdal

We reinterpret and generalize the construction of local Shimura varieties and their non-minuscule analogs by viewing them as moduli spaces of admissible pairs. Our main application…

math.NT2023

Compatibility of canonical $ℓ$ -adic local systems on Shimura varieties

Christian Klevdal, Stefan Patrikis

For a Shimura variety $(G, X)$ in the superrigid regime and neat level subgroup $K_{0}$ , we show that the canonical family of $ℓ$ -adic representations associated to a number field…

math.AG2020

G-rigid local systems are integral

Christian Klevdal, Stefan Patrikis

Let $G$ be a reductive group, and let $X$ be a smooth quasi-projective complex variety. We prove that any $G$ -irreducible, $G$ -cohomologically rigid local system on $X$ with finite…

Admissible pairs and p-adic Hodge structures III: Variation and unlikely intersection

Compatibility of F-isocrystals on adjoint Shimura varieties

Admissible pairs and p-adic Hodge structures I: Transcendence of the de Rham lattice

Admissible pairs and p-adic Hodge structures II: The bi-analytic Ax-Lindemann theorem

Compatibility of canonical ℓ-adic local systems on Shimura varieties

G-rigid local systems are integral

Admissible pairs and $p$ -adic Hodge structures III: Variation and unlikely intersection

Compatibility of $F$ -isocrystals on adjoint Shimura varieties

Admissible pairs and $p$ -adic Hodge structures I: Transcendence of the de Rham lattice

Admissible pairs and $p$ -adic Hodge structures II: The bi-analytic Ax-Lindemann theorem

Compatibility of canonical $ℓ$ -adic local systems on Shimura varieties