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The main issue of this paper is the discussion of Nielsen's realisation-problem for aspherical manifolds arising from (generalised) Seifert fiber space constructions. We present sufficient conditions on such 'model' aspherical manifolds M to have that a finite abstract kernel ψ: G → Out (π ( M)) can be (effectively) geometrically realised by a group of fiber preserving homeomorphisms of M if and only if ψ can be realised by an (admissible) group extension 1 → (π ( M)) → E' → G → 1. Then an algebraic approach to a (partial) study of the symmetry of M is possible. Our result covers all situations already described in literature and we show with an example that we also deal with other types of Seifert fiber space constructions which were not yet treated before. [ABSTRACT FROM AUTHOR]

Let L/k be a finite Galois extension with Galois group G, and $$1 \to A \to E\xrightarrow{j}G \to 1$$ a group extension. We study the existence of the Galois extension M/L/k such that the canonical projection Gal( M/k)→Gal( L/k) coincides with the given homomorphism j:E→G and that M/L is unramified. [ABSTRACT FROM AUTHOR]

We show that a p-analogue to the elementary type conjecture is not true. In fact, p-quaternionic pairings of non-elementary type are constructed for every prime p≥ 3. [ABSTRACT FROM AUTHOR]

We develop a modification of a notion of distance of an element in a valued field extension introduced by F.-V. Kuhlmann. We show that the new notion preserves the main properties of the distance and at the same time gives more complete information about a valued field extension. We study valued field extensions of prime degree to show the relation between the distances of the elements and the corresponding extensions of value groups and residue fields. In connection with questions related to defect extensions of valued function fields of positive characteristic, we present constructions of defect extensions of rational function fields K(x, y)|K generated by elements of various distances from K(x, y). In particular, we construct dependent Artin–Schreier defect extensions of K(x, y) of various distances. [ABSTRACT FROM AUTHOR]

Let p be an odd prime number, and F a nonarchimedean local field of residual characteristic p. We classify the smooth, irreducible, admissible genuine mod- p representations of the twofold metaplectic cover $$\widetilde{\text {Sp}}_{2n}(F)$$ of $$\text {Sp}_{2n}(F)$$ in terms of genuine supercuspidal (equivalently, supersingular) representations of Levi subgroups. To do so, we use results of Henniart-Vignéras as well as new technical results to adapt Herzig's method to the metaplectic setting. As consequences, we obtain an irreducibility criterion for principal series representations generalizing the complete irreducibility of principal series representations in the rank 1 case, as well as the fact that irreducibility is preserved by parabolic induction from the cover of the Siegel Levi subgroup. [ABSTRACT FROM AUTHOR]

We determine the action of the product of symmetric groups on the cohomology of certain moduli of weighted pointed rational curves. The moduli spaces that we study are of stable rational curves with m + n marked points where the first m marked points are distinct from all the others where as the last n may coincide among themselves. We give a recipe for calculating the equivariant Poincaré polynomials and list them for small m and n. [ABSTRACT FROM AUTHOR]

We prove a local-global principle for torsors under the prosolvable geometric fundamental group of a hyperbolic curve over a number field. [ABSTRACT FROM AUTHOR]

We prove formulas for SK( E, τ), which is the unitary SK for a graded division algebra E finite-dimensional and semiramified over its center T with respect to a unitary involution τ on E. Every such formula yields a corresponding formula for SK( D, ρ) where D is a division algebra tame and semiramified over a Henselian valued field and ρ is a unitary involution on D. For example, it is shown that if $${\sf{E} \sim \sf{I}_0 \otimes_{\sf{T}_0}\sf{N}}$$ where I is a central simple T-algebra split by N and N is decomposably semiramified with $${\sf{N}_0 \cong L_1\otimes_{\sf{T}_0} L_2}$$ with L, L fields each cyclic Galois over T, then [ABSTRACT FROM AUTHOR]

Abstract  In this paper, we study the algebraic structure of principal units in the tower of the maximal abelian extensions of local fields of characteristic zero and the corresponding Galois groups at each level. As an application, we show the finiteness result for the number of coverings with a given degree of the maximal abelian extension of a local field in characteristic zero. The number of p-coverings for $${\mathbb{Q}_p}$$ is computed explicitly. [ABSTRACT FROM AUTHOR]

Abstract??Inspired by work of G. Harder we construct via the motive of a Hilbert modular surface an extension of a Tate motive by a Dirichlet motive. We compute the realisation classes and indicate how this is linked to the Hodge-1-motive of the given Hilbert modular surface. [ABSTRACT FROM AUTHOR]

Using the theta correspondence, we study a lift from (not necessarily rapidly decreasing) closed differential ( p− n)-forms on a non-compact arithmetic quotient of hyperbolic p-space to Siegel modular forms of degree n. This generalizes earlier work of Kudla and the second named author (in the case of hyperbolic space). We give a cohomological interpretation of the lift and analyze its Fourier expansion in terms of periods over certain cycles. For Riemann surfaces, i.e., the case p= 2, we obtain a complete description using the theory of Eisenstein cohomology. [ABSTRACT FROM AUTHOR]

We shall study properties of groups having finite cohomological dimension relative to the family of all finite subgroups. We also compare these groups with those satisfying various suggested algebraic analogues to group-actions on finite dimensional proper G-spaces. [ABSTRACT FROM AUTHOR]

Given an arbitrary congruence function field K of characteristic p and a finite group G with a unique p-Sylow subgroup p(G) which is abelian and for which the factor group G/p(G) is nilpotent and has s generators, there exists a geometric Galois extension L/K with Galois group G in which precisely s prime divisors of K are ramified. [ABSTRACT FROM AUTHOR]

The focus of interest in this paper are geometric Galois realizations of finite groups. A tool to construct such realizations are geometric embedding problems which are introduced. Then the class of semiabelian groups having geometric Galois realizations is studied and characterized in several ways. In particular, a table of small non-semiabelian groups is computed. At the end, geometric Galois realizations of some small non-semiabelian groups are constructed. [ABSTRACT FROM AUTHOR]

The lowest dimensional Jacobi group G sets a link between the theory of Siegel modular forms of degree two and the elliptic modular forms of integral and half integral weight. This note is meant to help finding a way to associate L-functions to automorphic representations of the group G by using the approach via Whittaker models of these representations. Thus, here the question of existence and unicity of these models is discussed. This question may be reduced to a closer study of the Schrödinger and Weil representation of the Heisenberg resp. the metaplectic group and thus to the application of some results by Waldspurger. [ABSTRACT FROM AUTHOR]

A new invariant p( V) is defined for real algebraic varieties V which measures the complexity of semi-algebraic sets in V. p( V) is the least integer such that every semi-algebraic set S ⊂- V can be separated from its compliment by p( V) polynomials. This is a very natural invariant to consider. Using results of Bröcker [4-8] and generalizations of Bröcker's results found in [16,17], upper bounds for p( V) are computed. The proof is simpler than the proof of similar results in [5-9],[15-18] since the complicated local-global formula for the stability index and the various pasting techniques are not needed. Lower bounds for p( V) are also computed in some special cases, the technique here being to first study the corresponding invariant p( X, G) for a finite space of orderings ( X, G) [13,14]. [ABSTRACT FROM AUTHOR]