Related papers: On finite arithmetic simplicial complexes

We give explicit computations of the $\Gamma$-Euler characteristic of several families of orbit space definable translation groupoids. These include the translation groupoids associated to finite-dimensional linear representations of the…

We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description…

We compute the weighted Euler characteristic, equivariant with respect to the action of the symplectic group of degree six over the field of two elements, of the moduli space of principally polarized abelian threefolds together with a level…

We apply the Fixed Point Theorem for the actions of finite groups on Bruhat-Tits buildings and their products to establish two results concerning the groups of points of reductive algebraic groups over polynomial rings in one variable,…

For local non-archimedean fields $k$ of sufficiently large residual characteristic, we explicitly parametrize and count the rational nilpotent adjoint orbits in each algebraic orbit of orthogonal and special orthogonal groups. We separately…

The projective unitary group PU(n) is the quotient of the unitary group U(n) by its center. We compute the integral cohomology ring of PU(n) using explicit constructed generators.

In this article we study combinatorial non-positive curvature aspects of various simplicial complexes with natural $\widetilde A_n$ shaped simplicies, including Euclidean buildings of type $\widetilde A_n$ and Cayley graphs of Garside…

Let G be a semisimple quasi-split group defined over a global function field. We express the relative Tamagawa number of G in terms of local data including the number of types of special vertices in one orbit of the Bruhat-Tits building…

Based on the work of Conrad-Gabber-Prasad, the paper deals with the geometry of particular pseudo-semisimple groups, namely those which can be written as quotient of Weil restriction of semisimple groups. We establish that these groups are…

This is an announcement of conjectures and results concerning the generating series of Euler characteristics of Hilbert schemes of points on surfaces with simple (Kleinian) singularities. For a quotient surface C^2/G with G a finite…

We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant…

We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring $\mathbb{Z} G$ of a finite nilpotent group $G$, this provided the rational group algebra $\mathbb{Q} G$…

We show that the p-operator in the Witt algebra (the restricted Lie algebra of derivations of the quotient of the polynomial algebra over a field of characteristic p by the ideal generated by the p-th power of the indeterminant) is given by…

Suppose $4|n$, $n\geq 8$, $F=F_n=\mathbb{Q}(\zeta_n+\bar{\zeta}_n)$, and there is one prime $\mathfrak{p}=\mathfrak{p}_n$ above $2$ in $F_n$. We study amalgam presentations for $\operatorname{PU_{2}}(\mathbb{Z}[\zeta_n, 1/2])$ and…

We introduce Lehmer codes, with immersions in the Bruhat order, for several finite Coxeter groups, including all the classical Weyl groups. This allows to associate to each lower Bruhat interval of these groups a multicomplex whose…

Let $\mathbf{G}$ be a reductive Chevalley group scheme (defined over $\mathbb{Z}$). Let $\mathcal{C}$ be a smooth, projective, geometrically integral curve over a field $\mathbb{F}$. Let $P$ be a closed point on $\mathcal{C}$. Let $A$ be…

Using the geometric quotient of a real algebraic set by the action of a finite group G, we construct invariants of GAS sets with respect to equivariant homeomorphisms with AS-graph, including additive invariants with values in Z.

In this paper we study the mixed Poincar\'e polynomial of generic $\mathrm{PGL}_n(\mathbb{C})$-character stacks with coefficients in some local systems arising from the conjugacy classes of $\mathrm{PGL}_n(\mathbb{C})$ which have…

For a finite field extension $F/\mathbb{Q}_p$ we associate a coefficient system attached on the Bruhat-Tits tree of $G:= {\rm GL}_2(F)$ to a locally analytic representation $V$ of $G$. This is done in analogy to the work of Schneider and…

We prove a formula that relates the Euler-Poincar\'e characteristic of a closed semi-algebraic set to its Lipschitz-Killing curvatures