-homotopy theory.
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...
Cet article présente la construction de la catégorie homotopique stable d’un site suspendu avec intervalle arbitraire. La fonctorialité de cette construction est étudiée, avec des applications à la théorie homotopique des schémas introduite par F. Morel et V. Voevodsky.