Elmar Grosse-Klönne

Publications26
h-index9
Citations224
Highly Influential Citations22
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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…
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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…
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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…
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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…
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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…
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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…
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Sheaves of bounded p-adic logarithmic differential forms
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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…
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On the crystalline cohomology of Deligne-Lusztig varieties
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Integral structures in automorphic line bundles on the p-adic upper half plane
Abstract.Given an automorphic line bundle of weight k on the Drinfel’d upper half plane X over a local field K, we construct a GL2(K)-equivariant integral lattice in as a coherent sheaf on the formal…
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