Elmar Grosse-Klönne

Publications26
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Citations207
Highly Influential Citations25
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Rigid analytic spaces with overconvergent structure sheaf
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
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
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
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
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
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
TLDR
We describe a logarithmic F-crystal on Y whose rational crystalline cohomology is the rigid cohomOLOGY of X, in particular provides a natural W[F]-lattice inside the latter; here W is the Witt vector ring of k. Expand
Acyclic coefficient systems on buildings
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
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
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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