L. Mann

activity

20202022

most citedThe

p

-adic Corlette-Simpson correspondence for abeloids

9 citations · 17 across the 6 of their papers we have counts for

collaborators

6 papers

math.AG2022

The 6-Functor Formalism for $Z_{ℓ}$ - and $Q_{ℓ}$ -Sheaves on Diamonds

Lucas Mann

For every nuclear $Z_{ℓ}$ -algebra $Λ$ and every small v-stack $X$ we construct an $\infty$ -category $D_{nuc} (X, Λ)$ of nuclear $Λ$ -modules on $X$ . We then…

math.NT2022

$p$ -adic sheaves on classifying stacks, and the $p$ -adic Jacquet-Langlands correspondence

David Hansen, Lucas Mann

We establish several new properties of the $p$ -adic Jacquet-Langlands functor defined by Scholze in terms of the cohomology of the Lubin-Tate tower. In particular, we reprove Schol…

math.AG2022★ 6 cited

A $p$ -Adic 6-Functor Formalism in Rigid-Analytic Geometry

Lucas Mann

We develop a full 6-functor formalism for $p$ -torsion étale sheaves in rigid-analytic geometry. More concretely, we use the recently developed condensed mathematics by Clausen--Sch…

math.AG2021★ 9 cited

The $p$ -adic Corlette-Simpson correspondence for abeloids

Ben Heuer, Lucas Mann, Annette Werner

For an abeloid variety $A$ over a complete algebraically closed field extension $K$ of $Q_{p}$ , we construct a $p$ -adic Corlette-Simpson correspondence, namely an equivalence…

math.AG2020★ 2 cited

Normal and Irreducible Adic Spaces, the Openness of Finite Morphisms and a Stein Factorization

Lucas Mann

We transfer several elementary geometric properties of rigid-analytic spaces to the world of adic spaces, more precisely to the category of adic spaces which are locally of (weakly…

math.AG2020

Local systems on diamonds and $p$ -adic vector bundles

Lucas Mann, Annette Werner

We use Scholze's framework of diamonds to gain new insights in correspondences between $p$ -adic vector bundles and local systems. Such correspondences arise in the context of $p$ -a…

The 6-Functor Formalism for Zℓ​- and Qℓ​-Sheaves on Diamonds

p-adic sheaves on classifying stacks, and the p-adic Jacquet-Langlands correspondence

A p-Adic 6-Functor Formalism in Rigid-Analytic Geometry

The p-adic Corlette-Simpson correspondence for abeloids

Normal and Irreducible Adic Spaces, the Openness of Finite Morphisms and a Stein Factorization

Local systems on diamonds and p-adic vector bundles

The 6-Functor Formalism for $Z_{ℓ}$ - and $Q_{ℓ}$ -Sheaves on Diamonds

$p$ -adic sheaves on classifying stacks, and the $p$ -adic Jacquet-Langlands correspondence

A $p$ -Adic 6-Functor Formalism in Rigid-Analytic Geometry

The $p$ -adic Corlette-Simpson correspondence for abeloids

Local systems on diamonds and $p$ -adic vector bundles