A Comparison Theorem.
Let be a separated morphism of adic spaces of finite type over a non-archimedean field with affinoid and of dimension , let be a locally closed constructible subset of and let be the morphism of pseudo-adic spaces induced by . Let be a noetherian torsion ring with torsion prime to the characteristic of the residue field of the valuation ring of and let be a constant -module of finite type on . There is a natural class of -modules on generated by the constructible -modules...
We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions of "barred...