Let G be a connected semisimple group over a non-Archimedean local field. For every faithful, geometrically irreducible linear representation of G we define a compactification of the associated Bruhat-Tits building X(G). This yields a finite family of compactifications of X(G) which contains the polyhedral compactification. Besides, this family can be seen as a non-Archimedean analogue of the f...

We determine several necessary and sufficient conditions for a closed almost-complex orbifold Q with cyclic local groups to admit a nonvanishing vector field. These conditions are stated separately in terms of the orbifold Euler-Satake characteristics of Q and its sectors, the Euler characteristics of the underlying topological spaces of Q and its sectors, and in terms of the orbifold Euler cla...

A result of Chai–Faltings on Satake parameters of Siegel cusp forms together with the classification of unitary, unramified, irreducible, admissible representations of GSp4 over a p-adic field, imply that the local components of the automorphic representation of GSp4 attached to a cuspidal Siegel eigenform of degree 2 must lie in certain families. Applications include estimates on Hecke eigenva...

We derive an identity for certain linear combinations of polylogarithm functions with negative exponents, which implies relations for linear combinations of Eulerian numbers. The coefficients of our linear combinations are related to expanding moments of Satake parameters of holomorphic cuspidal newforms in terms of the moments of the corresponding Fourier coefficients, which has applications i...

We prove two results regarding Hodge structures appearing in the cohomology of complex tori. First, we that if a polarizable structure appears torus T, it an abelian variety isomorphic to subquotient T. Second, universality result for Kuga–Satake construction applied K3 type might not be polarized.

In this paper, we first generalize to any hyper-Kähler manifold X with $$b_3(X)\not =0$$ results proved by O’Grady for manifolds of generalized Kummer type. the second part, restrict type and prove, using Markman, that their Kuga–Satake correspondence is algebraic.

The topic of this paper is a generalization of Tannaka duality to coclosed categories. As an application we prove reconstruction theorems for coalgebras (bialgebras, Hopf algebras) in categories of topological vector spaces over a nonarchimedean field K. In particular, our results imply reconstruction and recognition theorems for categories of locally analytic representations of compact p-adic ...