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...

Let Γ be a discrete subgroup of a simply connected, solvable Lie group G, such that AdG Γ has the same Zariski closure as AdG. If α : Γ → GLn(R) is any finite-dimensional representation of Γ, we show that α virtually extends to a continuous representation σ of G. Furthermore, the image of σ is contained in the Zariski closure of the image of α. When Γ is not discrete, the same conclusions are t...