• Publications
  • Influence
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
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
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
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
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
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
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
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