Title:Â On the generalized Beauville decomposition.Abstract:Â Over 30 years ago, the work of Beauville and Deninger-Murre endowed the cohomology of an abelian scheme a (motivic) decomposition which splits the Leray filtration. This structure, now known as the Beauville decomposition, is induced by algebraic cycles obtained from the Fourier-Mukai coherent duality. In recent years, the study of Hitchin […]
Title: Isotrivial fibrations of hyper-Kähler manifolds.Abstract: A Lagrangian fibration of a projective hyper-Kähler manifold is called isotrivial if its smooth (abelian variety) fibers are all isomorphic to each other. Given an isotrivial fibration of a HK manifold f : X -> B with at least one rational section, we prove the following four descriptions of the fibration: […]
Title:Â Finite approximations as a tool for studying triangulated categories.Abstract:Â A metric on a category assigns lengths to morphisms, with the triangle inequality holding. This notion goes back to a 1974 article by Lawvere. We'll start with a quick review of some basic constructions, like forming the Cauchy completion of a category with respect to a metric.And […]