Let M be a complete nonsingular fine moduli space of modules over an algebra S. A set of conditions is given for the Chow ring of M to be generated by the Chern classes of certain universal bundles occurring in a projective resolution of the universal S-module on M . This result is then applied to the varieties GT parametrizing homogeneous ideals of k[x, y] of Hilbert function T , to moduli spa...

In [GM2], Goreskey and MacPherson defined and constructed intersection complexes for topological pseudomanifolds. The complexes are defined in the derived category of sheaves of modules over a constant ring sheaf. Since analytic spaces are of this category, any algebraic variety defined over C has an intersection complex for each perversity. The purpose of this paper is to give an algebraic des...

Drinfeld’s relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting of stable maps from nodal deformations of the curve into twisted flag varieties. As an application, we prove that the twisted intersection coho...

(i) is the most important one. We showed that extensions < = are classified by >@?A& 1 B DCE GF ( . The element 0 corresponded to a splitting. If one element is a non-zero multiple of the other, they correspond to the same , although different extensions. As an application, we proved: Proposition. Every rank 2 locally free sheaf on ? is a direct sum of invertible sheaves. I can’t remember if I ...

This paper studies algebraic frames L and the set Min(L) of minimal prime elements of L. We will endow the set Min(L) with two well-known topologies, known as the Hullkernel (or Zariski) topology and the inverse topology, and discuss several properties of these two spaces. It will be shown that Min(L) endowed with the Hull-kernel topology is a zero-dimensional, Hausdorff space; whereas, Min(L) ...

It has been long expected that there exists a deep connection between singularities of certain arc spaces and harmonic analysis over nonarchimedean fields. For instance, certain functions appearing naturally in harmonic analysis can be interpreted as the function attached to the trace of the Frobenius operator on what should be the stalks of the intersection complex of certain arc spaces, see [...

Let X be a projective scheme over a field. We show that the vanishing cohomology of any sequence of coherent sheaves is closely related to vanishing under pullbacks by the Frobenius morphism. We also compare various definitions of ample locally free sheaf and show that the vanishing given by the Frobenius morphism is, in a certain sense, the strongest possible. Our work can be viewed as various...