9 problems

Let $K$ be an algebraic number field, let $S$ be a finite set of maximal ideals of its ring of integers, and let $\Lambda_S^\times$ be the group of units of an $S$-localized maxima…

Let $G$ be a ${\mathord{\mathbb{Q}}}$-simple algebraic ${\mathord{\mathbb{Q}}}$-group, let $\{p_1,\ldots,p_n\}$ be a nonempty set of prime numbers, and write…

Let $k$) be a number field, let $\mathbf{G}$ be an absolutely almost simple, $k$-isotropic $k$-algebraic group, let $S$ contain all archimedean places of $k$, and let $\Gamma<G_S$…

Let $G$ be an $S$-arithmetic group in arbitrary characteristic, and let the filling functions and rank be understood as in the cited Lie-group theorem. The S-arithmetic polynomial…

Let an $S$-arithmetic group act on the product of a symmetric space and a Euclidean building. Denote the dimensions of these factors by the dimension of the symmetric space and the…

Let $T$ be a finite set of primes with $|T|=d$, let $K[1/T]$ denote the corresponding $S$-arithmetic level, and let $\mathcal{F}$ be the coefficient system used in the paper. Cyclo…

Let $T$ be a finite set of primes with $|T|=d$, and let $Y(K[1/T])$ be the associated $S$-arithmetic space. Eisenstein homology conjecture. Then $H_i(Y(K[1/T]),\mathbf{Z})$ is Eise…

Let $\Gamma$ be an $S$-arithmetic subgroup of a reductive algebraic group defined over a global field $\mathbb K$ such that $\Gamma$ acts as an irreducible non-uniform lattice on…

Let $K$) be a global field, meaning a global function field or a number field. Let $G$ be an absolutely almost simple $K$-isotropic $K$-group, let $S$ be a non-empty finite set of…