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Rigid analytic spaces with overconvergent structure sheaf

- Elmar Grosse-Klönne
- Mathematics
- 22 January 2000

We introduce a category of 'rigid spaces with overconvergent structure sheaf' which we call dagger spaces --- this is the correct category in which de Rham cohomology in rigid analysis should be… Expand

Frobenius and monodromy operators in rigid analysis, and Drinfel'd's symmetric space

- Elmar Grosse-Klönne
- Mathematics
- 1 September 2005

We define Frobenius and monodromy operators on the de Rham cohomology of $K$-dagger spaces (rigid spaces with overconvergent structure sheaves) with strictly semistable reduction $Y$, over a complete… Expand

Integral structures in the $p$-adic holomorphic discrete series

- Elmar Grosse-Klönne
- Mathematics
- 14 August 2014

For a local non-Archimedean field $K$ we construct ${\rm GL}_{d+1}(K)$-equivariant coherent sheaves ${\mathcal V}_{{\mathcal O}_K}$ on the formal ${\mathcal O}_K$-scheme ${\mathfrak X}$ underlying… Expand

Finiteness of de Rham cohomology in rigid analysis

- Elmar Grosse-Klönne
- Mathematics
- 15 May 2002

For a big class of smooth dagger spaces --- dagger spaces are 'rigid spaces with overconvergent structure sheaf' --- we prove finite dimensionality of de Rham cohomology. This is enough to obtain… Expand

On special representations of $p$-adic reductive groups

- Elmar Grosse-Klönne
- Mathematics
- 14 August 2014

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on… Expand

On the universal module of p-adic spherical Hecke algebras

- Elmar Grosse-Klönne
- Mathematics
- 14 August 2014

Let $\widetilde{G}$ be a split connected reductive group with connected center $Z$ over a local non-Archimedean field $F$ of residue characteristic $p$, let $\widetilde{K}$ be a hyperspecial maximal… Expand

On the crystalline cohomology of Deligne-Lusztig varieties

- Elmar Grosse-Klönne
- Computer Science, Mathematics
- Finite Fields Their Appl.
- 1 November 2007

TLDR

Acyclic coefficient systems on buildings

- Elmar Grosse-Klönne
- Mathematics
- 1 May 2005

For cohomological (resp. homological) coefficient systems ${\mathcal F}$ (resp. ${\mathcal V}$) on affine buildings $X$ with Coxeter data of type $\widetilde{A}_d$ we give for any $k\ge1$ a… Expand

From pro-$p$ Iwahori–Hecke modules to $(\varphi,\Gamma)$-modules, I

- Elmar Grosse-Klönne
- Mathematics
- 1 June 2016

Let ${\mathfrak o}$ be the ring of integers in a finite extension $K$ of ${\mathbb Q}_p$, let $k$ be its residue field. Let $G$ be a split reductive group over ${\mathbb
Q}_p$, let $T$ be a maximal… Expand

Compactifications of log morphisms

- Elmar Grosse-Klönne
- Mathematics
- 30 March 2004

We introduce the notion of a relative log scheme with boundary: a morphism of log schemes together with a (log schematically) dense open immersion of its source into a third log scheme. The sheaf of… Expand

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