No abstract

No abstract

No abstract

We study the affine formal algebra R of the Lubin-Tate deformation space as a module over two different rings. One is the completed group ring of the automorphism group Γ of the formal module of the deformation problem, the other one is the spherical Hecke algebra of a general linear group. In the most basic case of height two and ground field Q p , our structure results include a flatness assertion for R over the spherical Hecke algebra and allow us to compute the continuous (co)homology of Γ with coefficients in R. Contents

Let G be the group of rational points of a split connected reductive group over a p-adic local field, and let Γ be a discrete and cocompact subgroup of G. Motivated by questions on the cohomology of p-adic symmetric spaces, we investigate the homology of Γ with coefficients in locally analytic principal series and related representations of G. The vanishing and finiteness results that we find partially rely on the compactness of certain Banach-Hecke operators. We also give a new construction of P. Schneider's reduced Hodge-de Rham spectral sequence and show that the induced filtration is the Hodge-de Rham filtration. In a previously unknown case, our vanishing theorems then also imply two other of P. Schneider's conjectures.Mathematics Subject Classification (1991) 22E50 · 20G10 · 11F70