We construct a natural continuous map from the triangular spectrum of a tensor triangulated category to the algebraic Zariski spectrum of the endomorphism ring of its unit object. We also consider graded and twisted versions of this construction. We prove that these maps are quite often surjective but far from injective in general. For instance, the stable homotopy category of finite spectra ha...

In this paper we aim at the description of foliations having tangent sheaf TF with c1(TF) = c2(TF) = 0 on non-uniruled projective manifolds. We prove that the universal covering of the ambient manifold splits as a product, and that the Zariski closure of a general leaf of F is an Abelian variety. It turns out that the analytic type of the Zariski closures of leaves may vary from leaf to leaf. W...

We compare the behavior of fiber bundles with structure group G for G the general linear group GL, the projective general linear group PGL, and the general affine group GA. We prove a criterion for when a GA-bundle is in fact a GL-bundle, i.e., a vector bundle, over the Riemann sphereP1. We also discuss the behavior of fiber bundles under different topologies; specifically, we compare the analy...

We classify all locally finite joinings of a horospherical subgroup action on Γ\G when Γ is a Zariski dense geometrically finite subgroup of G = PSL2(R) or PSL2(C). This generalizes Ratner’s 1983 joining theorem for the case when Γ is a lattice in G. One of the main ingredients is equidistribution of non-closed horospherical orbits with respect to the Burger-Roblin measure which we prove in a g...

A complete extension theorem for linear codes over a module alphabet and the symmetrized weight composition is proved. It is shown that an extension property with respect to arbitrary weight function does not hold for module alphabets with a noncyclic socle.

In this paper we study the branching problems for Hecke algebra H(Dn) of type Dn. We explicitly describe the decompositions of the socle of the restriction of each irreducible H(Dn)-representation to H(Dn−1) into irreducible modules by using the corresponding results for type B Hecke algebras. In particular, we show that any such restrictions are always multiplicity free.