We generalize Nakamaye’s description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension . We also generalize Ein-Lazarsfeld-Mustaţă-Nakamaye-Popa’s description, in terms of valuations, of the subvarieties of the restricted base locus of a big divisor on a normal pair with klt singularities.
Let be a field and be the Grassmannian of -dimensional linear subspaces of . A map is called nesting if for every . Glover, Homer and Stong showed that there are no continuous nesting maps except for a few obvious ones. We prove a similar result for algebraic nesting maps , where is an algebraically closed field of arbitrary characteristic. For this yields a description of the algebraic sub-bundles of the tangent bundle to the projective space .
Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined symmetric...